{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "#sys.path.append('/home/luca/GitRepositories/Brancher')\n",
    "sys.path.append('/home/lucamb/GitRepositories/Brancher')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Brancher for time series analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we will show how to write time series models using the symbolic interface of Brancher. For simplicity, we will focus on simple examples with scalar variables. We will cover more complex models with convulutional and LSTM components in more advanced tutorials. Note however that the syntax for specifying those more advanced models is identical to the syntax shown in these simpler examples. Discrete probabilistic time series models are specified by an equation that links the parameters $\\boldsymbol{\\theta}_t$ of the probability distribution of the current value $\\boldsymbol{x}_{t}$ to the previous values of $\\boldsymbol{x}$:\n",
    "\n",
    "$$ \n",
    "\\boldsymbol{\\theta}_t = \\boldsymbol{f}(\\boldsymbol{x}_{t-1},...,\\boldsymbol{x}_{0}) ~,\n",
    "$$\n",
    "\n",
    "where $\\boldsymbol{f}$ is an arbitrary function. \n",
    "\n",
    "# Autoregressive models\n",
    "Gaussian autoregressive models are among the simplest examples of probabilistic time series models. An AR(1) model is specified by the following equation:\n",
    "\n",
    "$$ \n",
    "\\boldsymbol{\\mu}_t = b ~ x_{t-1}~,\n",
    "$$\n",
    "\n",
    "where $b$ is the (scalar) autoregressive parameter and $\\boldsymbol{\\mu}_t$ is the mean of a Gaussian distribution with fixed variance $\\sigma$. We also need to specify an initial distribution:\n",
    "\n",
    "$$\n",
    "x_{t-1} \\sim \\mathcal{N}(0, \\sigma)\n",
    "$$\n",
    "\n",
    "Let's write this model in Brancher!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from brancher.standard_variables import NormalVariable\n",
    "from brancher.variables import ProbabilisticModel\n",
    "\n",
    "# Model parameters #\n",
    "T = 100 # Time horizon\n",
    "b = 0.8 # Autoregressive parameter\n",
    "sigma = 1. # Standard deviation of the Gaussian input\n",
    "\n",
    "# Initial distribution\n",
    "x0 = NormalVariable(0., 1., 'x0')\n",
    "x = [x0]\n",
    "\n",
    "# Time series\n",
    "names = [\"x0\"]\n",
    "for t in range(1,T):\n",
    "    names.append(\"x{}\".format(t))\n",
    "    x.append(NormalVariable(b*x[t-1], sigma, name=names[t]))\n",
    "AR_model = ProbabilisticModel(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Done! Now we can use the model for generating and plotting some time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb445373cf8>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4WduUP4ypbBE+do4eqMk8nDwjrvwgbH8vaOLSgM4kKmpGTuS3v0LstZug47GCLnW5oXN4GpUE6+N2vAraq8V35ey4B4NOdOZWZCH2fqdv8S90Br588Mt0ObuKeswN9g18even896+t7eXY8eOsWfPnqJex2UXsYdjYX546ofcsuoWvrL3Kxi1Rq6ovWJWxK7IMAoUOUZE7HFib9oNV/8pHP8J9L6U9Zyp1gIlZMfQlJ8D5528bUfjLDdMpXV8URKo0bCoSc+n1DEVmhl6b93W/KUY74TwnKlYDUGXkPdWKDqHp2mtMiXIW0F7tQkQteyZuk4VlBs0KypiV+DxeHjHO97B17/+daxW69w7FIDLLmI/7zpPKBbippabUMf9OXbV7mLfwD7GfeNUG6sZdA+yo3pH2n7bqrbx4OkHBUlPxZc9ZWZ446fh9V8ISeajL2Q8p1LyeHbqLNuqty3eL3eZwekNoZakRJPJL18T1Uhv29Ewa1slYl+UWvbJCxCL5J84zYa6reKz4J8Cgy33tt4JMFWBJT431zMKFa0LO/9lis6RabY1zX6/bEYdlSYdZ8c9CZkmlxRzse2xC4msi41wOMw73vEOfu/3fo+3v/3tRT/+ZRexdzo6AdhkTy67lWlIR0aP4Aq6cIfdNFnSk2hvbX8r9912H83W5mTErjODzgibfxfGOrJWyDSaG9GpdKWIfQbu+f5BrvnSM3zr2R78oSiPHBtkR7ON1irTrG1TpZj54NvPneG/92V5/x15mH/lg7qt4nH09bm39Y6DqRrMwpJ4pSZQpwNh+p3+RGPSTCiVMY6cEbuWaEzGu1j5l0sMsizz4Q9/mI0bN/LJT35yUc5x2RF7l7MLg8aQ1mS0wb4Bk9bEoZFDiVLHmVKMRqVJRttK8lQXJyBLPURD4J/MeE6NSkNreWuplj0FvlCEU0MuLHot//qb0+z9ynN0jbi5K0O0DqKOHebv8PiLowM8cWo484tKqWOxiD0fOcY7LmrhzcKSeKUmULuGxbzSrMReY+LsuBenJwhkj9hh5XSf7t+/nx//+Mc8++yz7Nixgx07dvD4448X9RyXnRTT4ehgXcW6hAwDgnh31uzk8Ohh3tDwBmA2sadhJrErUZd7BIyZB8y2l7dzYiKZWJsOTfOxpz/GJ674xIq09O0cnkaW4fN3bcGq1/CFxzvxh6LcsT0LsSci9sI1dlmWGZoKZF+mT/SAwZ71b5c3zLUiCs+H2H0OUSKZ+tlZgVCsBGaWOiporzbj9PZzbsKLJJFxNGKC2H1hGm1zGLgtA1x33XWLV/Ybx2UVscfkGF3OLjbaN8567aq6qzjnOsfJcfGlVLpOMyKYIsWAiNhBzMHMgjZbG4OeQXzxNvL7Ou/j5MTJNLJfSTg5ILxztjaWs6etkkf+5FoO/M3NVJlnN6AA6LVqyjSqeUVlU74w/nAUdyDLvo6zC9fXASQpnkCd428qy3EppkrcCCTVoksxHUPTfPu5M4tOCIWic3iaCqOWWmvmv3tbPIF6qHcSm0Gb1tugwGqY/02/hMy4rIi9392PL+JjY+VsYt9VuwuAx849hkVnwarLkWVOaOyKFKPopNmX02tsYpl/fvo8npCHH3f8WOwS8mTdZznj1NA0VWZd4gutUklzljGWG+ZnBDY4JSpOprN1Jzp6Fi7DKKjbCuNduS19g9NCujNViQEbxqpFl2LuO3CBrzzVzStnL60xjZ3D02yst2ZdTSklj10j0xllGChZ9y4GLitiVxKnmSL2jZUbMWqMTPgnElYCWRHygqQWnYoA5nhlwxwRO4gxefd33Y875EYjafCEVyixD7rY0lheUBWDzaidl8Y+FCd2fzhKeOZsTM+YINXq9QUfNyPqtgnSnjidfRvFTsAU98Ix1y46sXePCC37O89fOnmeSDRG18hsK4FUNFUY0alVyDJUZrATgIuvsV9qq55MWOg1XlbE3uHsQKPSJKLnVGhVWnbW7ATm0NdBELvOLJbeICpjysrBnf3L2WxpRqPScGL8BP/T8T/sbdpLnakOd8g979/nckUgHKVnzMOWhvK5N06BzaCb13J72JWch+kOzIjaL+wXjy3XFHzcjEhUxuToQE0Qe9wLx7K4xC7LMt2jbix6DS+dmeC1/qlFO1ch6HV4CUZiOYldrZJorTICmROncHGJXa/X43A4Lmlyl2UZh8OBXq+f9zEuq+Rpp6NT2AOotRlf31W3i/1D+2eVOs5CyJOUYRRY6nJG7FqVllZrKw/2PEgkFuGj2z7KP736TysyYu8acRONyWxpLKypotw4vw5DJWIHsVxPI4je/aA1QcOODHvOA/Z2sZIbOQnb7868jdJ1mhqxj3UW5/wZMOQK4A5E+Ou3bOA7z5/lO8+f4b9+f9einS9fdI+Iz/6GOkvO7dqrzZwe9WTsOgUwl2kumnVvU1MTAwMDjI+PL/q5FgK9Xk9TU56+RxmwYGKXJKkZ+BFQC8jAd2VZLrpdmSzLdDm7uKnlJj78w0Nct7aKP7h2ddo2Sj373FJMJmKfO+pqK2/jzNQZrmm4hm3V2zDrzCtSYz85KBKnWxoLjdi1nJrHl3cwhdhnR+wvQ/NuyHKzLxhqjbAmGDyafRvFAMwYj9jNNUISisXy96opAN0jovLkilUV3HP1Kr7x7Bl6Rt2src1NqIuNXoeoLludoW8hFYrOnqmGHYR1r1V/cbpPtVotq1evnnvDyxzF+BRGgP8ry/Im4A3AxyVJKsC0Iz+MeEeYCk7RZFzDM11jHO6dXXO+rWobn7v6c7yl7S25DxbyZiD2+pwRO8CaCiEBfWz7xwAwa824wytPinl90IXNqC24NG0hGrtOIz6qqTM08Tlh7HVYdW3Bx8yJtbdA3yvgzNIQlYjYFWKvg1g4ax/EQqFExutqLXzw2tUYtGr+44Wl19ovOLxUW8rmTJq314jvWjYpBlaede9iY8HELsvysCzLR+P/dwOdwBwid+HocApby2hAHFrxnkiFJEm8c907c1fEgCD2shnRjrlW1CLn0N7uXn8337jxGwkt36KzrMiI/dSQi60FJk5B1DD7w1GCkcI6DIemAqyrFVFfWslj3yvisbXIxH7lB0UJ4+EfZH7dOyFyMorXzCI3KXWPTNNQrqfcoMVu0vHe3S08enxoSYyzUtHr8NFaaZxzu7U14rtWk6UkElaew+Nio6jrRkmSWoGdwIFiHhdEx6lKUjE4JjwpJhdiJpVRisndfQpQoa/gxpYbEz+btStPiglGonSPuNlcYOIU5pckC0djjLkDrK8VN+u0ksfe/aAug8YrC76WnLA2wIbb4diPM5t7ecfBlBz7l7QVWBxi7xpxsz5Fx77nmlVEYzLPdy+tjcEFh5dVlbllGIDNDVb+6/ev5JZNtVm3WWme7IuNohG7JElm4CHgE7IsT2d4/SOSJB2WJOmwkrg4NHKIv9v/d0Rjc0dwnY5OVltXc+yC0PUWRuyZpJjCOwjNOjOesIeYHJt742WCnlEP4WjhiVNI7zDMF6PTAWJyMkGXJsVceEn4qs90aSwGrvpDcZN//eHZr3knkolTWFS/mHA0xtlxD+tSiL25wohOo6J/cukcJX2hCKPTwbwidkmSuHVzHWUaddZtyg3aUh17EVEUYpckSYsg9ftkWf5Fpm1kWf6uLMu7ZFneVV1dzaGRQ/zJb/+ER848kjb9KBs6HZ2ssa2nY2gajUpi0ruAaTzBLBE7gCd/YrdoLcjIiW7UlQAlcTrTbz0fzMcIbGhKlDqurTUjSTCtJE8DLlG5UmwZRsHqvVC1Dg59b/ZrM4k90eBWfFuB3gkv4aicVnmiUkk0VRiWVIrpi587n4g9H1zKUsxTvU9xaOTQUl9GQVgwsUtCaL0X6JRl+Wv57OOL+Pj4Mx9P/OwKuXJuP+GfYMw/holVxGS4ur2SUDQ2fzc4pY49FfPw/FCGbqykksdTgy4seg0t9rkjtZmYjxGYUurYVGHEXKZJRnV9B8Rou1VFql+fCUkSUfvgkdkVMoqdgAKdWXizL0LE3hVvTFKkKAXNFUb6J5eO2HsnxLlbi0zsl1p9+ZhvjL9+8a/53skMN/hLGMWI2K8Ffh+4SZKk4/F/t+XaoW+6j1pjLZ+/9vMATAVzN1wcHRVfLK+7DrVK4k0bBQlPZkigzglZjmvsM4hd8dWeB7GvpCalU0PTbGkoPHEKKRF7ATKaUurYYNNj1WuTUsyF/aDSimEpi4Xtd4sa+cP3Jp+LxYQBmDGF2CUpXvJYfI29e8SNWiUlKksUNNsN9DuXToq5EC91bMlDiskHl6p17w9f/yHhWDgvVeFSQjGqYl6SZVmSZXmbLMs74v9yelCqVWq+9zvfSwywcAVzR+y/OPMLaow1XBiqYXODNVFmNy+dPewH5NlSjM4EZdaCiN2iFcvjlRKxh6MxOoen56WvA4mBHIUsuYddfiqMWow6DRa9JlnHfmE/NF4huoYXC/py2PZuOPlgMqkemAI5mi7FgCh5XASHx64RN6urTLP06eYKIy5/OD3ncBHR6/BhN+kSeZOF4lK07nUGnPy8++cAjPsv7YammVgSS4FWayu1plrKy4ROm4vYBz2DvDz4Mm9rv4sT/W6uarUnOtgylTzOiZmWvamw1BWkk660iP3MmIdQJDavihgAS7zDsDApJkB9ubiRW5UEW8gLQ8cWT4ZJxZX3QCQAHb8UP8+sYVegNCkVGadH0ytiFDTHpbCl0tlFRUzxbqrzSawvNn7S8ROC0SB3tN2BK+giGA0u7QXt/0bemy4JsWtV4o+YD7E/3COqEjaY3kQwEuOqVnui0WFeEbtCwpmGUiu17HkiEbGvkJLH06PivdtQP7+OR0mSKDdoC/KLGZry0xBfoVn1WoJ+Lxz4LzEKb9V187qOglC/Q9gMnHpI/DzTJ0bBIhiBeYMR+pw+NmToMG2uUIh9aeSYCw5f0fR1uPQidlfQxf92/S+3rLqF3XVC7ltSOSYShKf/Lu/Nl9QErExdhkFjyErskViEh3se5trGazk7LMh8V2sFdqMSsc/jQ5AzYq8vJU9zoGfUg1olzdlCngu2AjsMB6f8NNr04B7lvdP38sOpD8Iz/w8arrg4EbskwZZ3QO+LwiRupk+MAkutkGkixYvqlBtp5ohd3OwGliCBGoxEGXL5ixqxWy8xYr+/6368YS8f2fYRao0ipzfuW0I5psDV4JK7O5aXlWdNnr448CJj/jHeue6dHOp10lZtospchkWvQSXNc+K9QuxlGSJ2y9zdp6kwa1eWFNMz5mZVpTFnPfJcsBq0ef/d3IEw7kBEROyPfIwbHQ9wmI1wz2PwR88urr6eii3vEBU4HY9mJ/ZFaFJSrHo31M3OaZQbtFjKNEsixfQ7/chy8Spi4NLyZPeFffyk8yfc0HQD6+3rqTaKv/WYfwkjdu/lRuy68qzljg/1PES1oZrrGq7ncK+T3a1i9JlKJVFh1M1TY58xPSkVlnqIBkXklQcMGgNqSb1yIvYxD+tqFmY8ZTPmqFceOgYvJitmFbveBpsBRk7RUXM7Hwl+gtiq65OWyxcDNRugZjOcejAuxUhiFF8qFqFJqXvUjVGnpqlitiePJEk02Y2Zm5TyaPhbCJSKmKJq7PNIrC8WDo8exhV08b6N7wOgxigsI5Y2Yi/s3EtP7GXlGaWYEe8ILw6+yF1r7uL8RIDpQISrWpNfpgqTbp4a+2wp5of7z/PHPzlScC27JEmYdeYVEbEHI1EuOHysrc1wQywANkMOI7ATPxMyS/xvpJQ6NpoB7xh+cwsxGbyhJTCL2vJ26D8gbj6GCuECmYrEZye3kVwh6B4RDo6qDOPkAJozNSmdex7+uRm8izdpqddR3Bp2ALNOrMIvBWI/MX4ClaRie/V2AKw6KzqVbomJvbCV4CVL7A+feZiYHOPta9+eWJKm2sRWGLXzi9iDM8biAY8cH2Lf6fGU2acF6Oxa84qI2M9PeInG5AVbxdqMuuxSTCDuROE8DySbk5oRH+qItQXIYN17MbDl7eKx5zezZRiAilbxmM0Rch44M+ZhXU32G2mz3cjApD+9qWesE8JemDxftOuYiQsOL1a9JtGXUAyoVNIl4xdzauIUa2xrMGrFikSSJKqN1Yz6FndKVk6tebYdAAAgAElEQVRcdlJMFmI/NXGKdRXraLI0MRBfbqZ2O1YYdfOygE1G7OILEwhHeX3IhTcUJRRfchVUGbNCHB5Pj4rfcW0OoskH5QYt04EI0ViGPIbyOYiT49CUH7VKwh4SUXAsTp5LUrttbxMJW+TMxG6wiaYlR3HsdMPRGOOeIPU5rJGbKwz4w1EmPCk3Sp9TPBZJEopEY3z+Vx2JRC7EXR2rTPNqUsuFS8FWQJZlTk6cZGvV1rTna421S1vL7hkXjqJ5YsmJ3VZmwxV0zWolnvBPJLStPoePKnMZBl0yaWc3FUdjPznoIhwV53ap41JPActpszYuxXjGwTVQ+PVcJjgz6kYlJafOzxdKlJcxSZaI2AWxD08FqLPqUbv6ANDYW+P7LpFv99Z3isdUZ8dUVK4pGrFPeILIMtRZs49HS9Syp1bG+OPEXmCElw37zzq496Xz/O0jpxLf0Wyujv/nmf/Do2cenfe5FpvYI9EYh3qdObfpc/cxHZqeRezVxuqllWK8Y2DOEFBkwZITe7munIgcwRdJ1won/BNUGUStcP+kjxZ7euSiaOwFe0skBlkLR8AjF5I2vVMRHegsBelZisMjv/4k/PyDhV3LZYTTox5aK2d3QBYKW64kWTCd2EWpowEme0FrwmATOrZ7ibot2fy7gJQ5YgeobAfHmaKcaiSeOK4rz+5cmbFJKRGxF4eEHjk2CMDB805eOD1OOBpjYNI/y9VxxDvC8wPPc2zs2LzPtdjE/rPDA7zrP1/hzFj2FfaJ8RMAbKnakvZ8taF6aevYPWNgqsl786Un9vjyIrXkMSbHcPqdacTePMN0qsKoJRyV8QQLjN5mDLJOI3Z/eM7ZpzNh0calmIkemOov7FouI/SMuRecOAWwxyfVj04HZr84I2IfcvlpsOkFsVe0YombiC1VGz3WBnj7f8Puj2Z+vbJddC4Hc0tzLl84sxSVAuX9qc0RsSvVMgOplTFFjNi9wQhPnhrhnVc20Ww38C9PdtPv9BGNybMi9uNjxwFmBWiFwDpP694pX2jOSBzg2S4RsJ2f8Gbd5tTEKQwaA2tsa9KerzHW4Iv4csuuEz0wcCS/iy4UnsstYs/QfeoKuojIEaoMVUSiMYamAolOOwUVxsKdAgHReRpPnMqyzNELk6yPJwSnfAqxFxaxu8NumOoTszBjy8+bPRiJ0uvwJSbhLASK/Wzn8CzL/mTEPtlLNCYz4gqIUsfJXqhYhVUvKlGWTIoB2PYuqF6X+bXKOBk4s8sx/lCU6/7lWR48kjsIUCL2XMRu1GmoMuuyROwLJ/anO0bxh6O8e1czn7xlHR3D03znefG7zYzYlUjdn2kwSZ6Yb8T+o1cucPd3X825kgtGorx8VlQKKeWamXBq4hSbKjehVqWvTBVZOGct+2//Ae5/z+JwgHcsWXmVBy5JYp/wi7btSkMlw64A0Zg8yybWPl+/mJQhGxccPhzeEDdtFH+0KV+o4IjdrDXjDXmRw17R5p5nDfzlhN4JX7wiZuERe42ljCpzGaeGMhG7W4ykcw0wNjlFOCpTX66HqQsiYtcLGWfJpJi5YBemdrnkmAtOL+5AJOFnng2j7iBatZToss6Gppn2vYpZmXfhUszDxwZptBnYtaqCO7c3sr7WwoNHRB5pZsSeIPbIwom9UHl1ZFpwhFI9lwmHzk/iiztHZmvqCkVDdDo72Va1bdZredWyu0fE+z7yWgFXnwciQTF/4HKSYmxlYtRdJmKv0lclvgBNGTR2AGehtewhb6LrVJFhbt4g3jCXP5z0/Mjzw2XRWYgRw6dUCBThC3WpQamIKEbELkkSWxqtnBqcUQkVCQmzrcq1gMzBo4IodlVFIOyDilZ0GhV6rSo5bONSg71NPDqylzyen3Cjr/8Z592v5zzUqCtAjUWftYZdQbPdmO4XoxD7Ajtgx91BXuwZ566dDahUEmqVxF/euh4Ak05NlTl5w/GGvXRPdgMLk2LKDVoiMTlBwPnCGa8KyrgKjOP57jF0ahWrq0xZb6qnJ08TjoXZUrWFV885iKXIZdWGePdpLp1dkb/O/Lag658TyurrcpdiEsRuqErcXWdG7EkpZj4Re5zY+yaxlGnY2VKRdB201AuCyTPytugE2blV8bdyGRJ7z5inKBUxCrY0lNMz5iEQTvkCKzJMvWgKee3EMTbWW9lQFm+0iZc6WvXaSzdi1xnB2pQzYj80dByt7Siv+36e81Aj0wFqcwx/VtBcYWBoyi80+0goWfW1wOTpY68NEZPhrh3JufRv2ljDVa0VbKy3ppU6nhg/QUyOYdFZFjRNbL5GYMqqvWM4e8T+/Olx9rTZWV9ryUrsSuJUCrVw93df5ZmuJIkrtgI5Sx4Vg7gzzxRy+XNDuWFcThF7uW528tThF1/mKoOI2DUqKWHdqmDeRmApg6yPXphk5ypB6jbFdTAxcCO/iCdh3buciX3UzapKE3rtwipiFGxptM5eOgfiN/aGHQBIznO8Z1cT0pQodcS2CgCLXrO0GvtcqGzLSezHnS8D4JRfZ8CdvTx2ZDpAXXl2fV1Bs91IJCYz7PInE6eWBtETEM6QoM4TjxwfZEujNa0hTZIkfvgHu7n3nqvStj0+dhwJid11uxccsUPhxO7wCuO1bBH7wKSPM2Me3riumpZKYcMQy5C8PjVxiipDFcMO8b6n1u6btCZMWlP2iD3oESvLMiv0HwR/ESVZ5SZ9OWnsWrUWo8aY5hcz4Z9Ar9Zj0pron/TTWGFAPWNJatELb++CpyjF551OB8J0j7q5sqUCEF4VU76wqHwA0ZqdBxLWveo46Sl37WWEnjHPghuTUqH4uZ8aSpFjlIi9ohW/2kKbaoy7djaKxCmATXSdWg3apauKyQeVa3ImT/sDR4gGakGW+EVPxvHAAIxNB3MmThWk2fcqiVMluTvPIOPMmIcTA660aF2BqUyT8HVRcGzsGGsr1lJtqF4QsdsWGLF3j7gzVhs93y3ehxvW19BsNxKKxBhzz3bhPDlxki1VWxIBx7nx9CRrjbEmO7Er7/Xmu8Qgljz5Iy94L0MpBmZ3n04ERA27JEn0OX2zKmJAMQLTzk9j15k43jeFLMOVqwSx25SMfNNuaLsRnvrrzBPqZyARsZc3AdKyi9hDkRi9E96iJE4VNFUYKDdoOTWYEmHFSx1DGjPnojVcYXFiM+oEsZvrEk6OYjzepRyxrxE6t292+d2QZ4iANEjYtYuy8GYePfMokdjs38UTjOAJRvIj9njuqX/Sl4zYqzeIxxklj95ghLFMZaYz8NDRAVQS3Lm9Yc5to7EoJyZOsLNmJ0atcUFVMfOx7o1EY0z6wjSU6/GHo5waHuLmn93My0MvJ7Z5vnucpgoD7dWmhKQ7U45xBV30TveyrWpbktgn0ksbaww12ZOnyvd+/W1i8taZp/P+HeaEki+5nKQYSHafKpjwJZuTBpyza9gT++XyHcmGuMZ+5MIkKgm2N5cnjjXpCwlzp7vvg+Y98NAfwumnch4uEbGbq8BYueyIvdfhJRKTWbdAj5hUSJLE5gYrHRki9lcGw5yN1tCqin+Y4xUxCix6De5LwE8kKzJVxsgyBKZ5vu8FACKeDUiePYz5x3hx4MVZh0g0J+VB7A02AypJfE+SEbtIcs7U2b/4eCd3fPOlnDX0wUiUnx3q5+aNtdTkcf6eqR68YS87anZg1BgJxUKEY/P7+8xHipmMlztft1bwxVNnX2HMP5aYkyzKHCe4cX0NkiRlJfbXHSKZvaUyGbHPrHevNlZn19iV772lTgSGZ57JuwBjTih2Atq5/x4KLglit5ZZZyVPqwxVeIMRHN5QIiqZCXuh1r0pg6yPXJhkfZ01UUKX5jqoM8H7fgq1W+Cnvw+9L2U9ZGLYhsEmOhKXGbH3xD1i1hRRigFh6NY54iYcjdf8xiP2R7s8OHVN6L2DIhkYr2FXYDVcBhE7pFsLHP0RfKmZffu/SGVIwwdVrxOZaqXKUMVDPQ/NOsRYHs1JCrRqFfXlBmHfO0fE/so5B2PuICcGsuu/T54aweEN8Xt7WuY8NyTLHJWIHeZf8liey24iC5Tv/57VlahVEkfj19PvFn0Ch3tFmeMN64WM0Ri/Ec4k9pPjJwGwa9txByO0VZuY8oXT+KXaKLpPM5ZjelISnGveJEqmxzry/j1yokA7AbhEiL1clz5sYyIwQaWhMlGfm0mKAagwaZksJHkaH2Qt60wc75/iihZb8hqM2vR5i/py+P2HxfCN576Y9ZDmeDOCW28S49KWmcZ+Ou4R015dXGLf3GAlFIkl27vjEftzvQHq2zYhyTGhVbsGZkXsl7TGXrFKWFakRuyH78VXsYqDWokbfV4+x3f5i+hPuLP9bbw4+CIj3nTTuZEEsc9dFQOiWunAOQchd/yzV6VE7Elin/KFEprxc93Zg4/7DvTRYjeyd21mIvnWsW9xzxP3JBK/x8aOUWOoocHUgEEjArD5VsZYyjTotaqED38+UBKn9TY9bVUmLnhF5K0Qu1LmeHW78PfRaeI3whnEfmT0CGtsa+ifEKR92xbh9Ho+RY6pMdQQjoUzDwZKHZm45k3i/z1FkmM84wXJMHCJELutzMZ0KK6xRkO4gi5REePIXOqooMKoK0xjj5eC+dDjCUbSyMpm0OEORpIRJIDRLvxB+g9mbRM3uMdRyzIerX5ZRuz9Th/15YaiVcQoUCyYE/Xs8Yjdg4GdO64Qz53fB8hpxG7VawlFYumlklkQiUV49Myj85YG5gW1VpC7Quwjp2D4NQ5svo2wJPMj18c5Xv1W3qN+nlvt1xCTYzxy5pG0QyjEnk9VDMCf3byWIVeAI51nQV0mPrc6S9pn8VifICOTTs3z3ZkTgKdH3Rw87+R9e1qy1s+/MvwKR8eOcvev7+bV4Vc5PnacHTU7kCQJo2ZhEbskSbRWmujN0fI/E0pEXWkqY12dHo/cCwgzr2hM5vGTI1zdXolRl/TPb7Eb0yL2UDTEsbFj7KnfQ3e8EubNW0R13NmUBGqi+zRTAtU7JoJBTRlY68Vqv1j17J7RyzRijydP+51exrwpNexxD4xsGnuFSWjseXeqxYl9MiyWfA0plqhZXQfbb4JYGC7sz3hIydWPORbDrdYuS2LPt+yuUKyuNGHSqXk93oHqmXbgk8u4dWszNas2iY3OPiseU4ndoHSfzi3HPN//PH+7/2/57YUiN4zMhdTKmOP3gUrLCzoJrWRAHWpjaPMfoyFC08mH2V23m6d60/M4o64AFr0mjYxy4apWO7+3p4WBoUHCZTbhg2SuTovYj/aJnNLvX93KiQEX4xmqQu579QI6tYp3XdmU9Vyj3lF21+2m2lDNR5/+KMPeYXbW7ARISDELqYxZXWXifI6W/5lwxJuTKs067PYxkKJsr9qJK+jiyc6zDE75efeu5rR9ZhL7a+OvEYgG2FO3h87haZoqDGyos6BVS2k6e6L7NJPOPtOka83N0Peq6KZeKAq0E4BLiNijcpQ3ff0pvr1PaGRKc5K5TENFFkN/u1FXmBFY3It9IqQQe5KwFGKfmknszW8AjR7OPpf5mK5+zDEZjyru+hdwCW14mWBkOpBXEq9QqFQSmxqSHainzg3ixsin37xBvI86czK3YUvR2BW/mDzkmAPDB9IeLxoU+95ICE78FHndm9k3cgCrvJkWuxVVVTu/il2N6eT/sM7SMkuKGZ0OFvyef/otG6jV+BgIGsSq01QzK2LfUGfl9q1CYth3Op2cfKEIvzg6yFu21lFpziwBRWNRJvwTbK/ezn233cfNLTejklTsqd8DkIjYF9Kk1Fplot/pIxLNz2/F4Q0hSWL1HisTw0W2V9wMwP8eOUalScctm9JJsaXSyLg7iD/e4frq8KuoJBW76nbRPeJmQ50VjVpFi93IufHkSj3RpJSpMsY7ke76uXqvCAiH5u92CczLTgAuIWIHCMlenuzqAZLE3lRhyGror9gK5K2zx4l9LE7sqU1PtmymYlo9rLoGzmUh9qk+LLKMRw4LfQ2EGdgywagrQE2eWm+h2NxQTsfwNCcGpnA4xlEbrGJ1JklgXy1WWGpdcrIVQoqB/CL2gyMH0x4vGuxtolnl6P+Az0HnuhsZ948T9W5kld2I1aDhO5E7UYe9VI+fwRP2pJGh6DotjNitei1b7DFGQkb++8VzaRF7NCaLnNIqG5sbrFSZy3h+BrH/8vgQ7mCE979hVabDA+AMOInKUWqMNRi1Rr76xq/yzLueYW3FWoCExr4Qv5jVlSbCUTkxFnEuOL1BbAYtapXEeKibWLAKAq0AHB7s4R1XNqHTpNPcTB/7A8MH2FK5BZ3KyLkJb8KobnWVOS1iV2wFMk5SmpngrFwbv8AFTrJSbs6XpRQT7z6V1D48EeF1IaQYX1Z9HUhE8nnr7HEpZsSnRqdRUWlK+l0kmyMyHKvtRhjvAtfg7Nem+jCrdLhDnuQde5nIMe5AGG8ouigROwid3ReK8okHjlOhDmCrSBlgofiu2FaBKvkxtRoUh8fkDXjcHUzPjSCiqnOuczSaG+l39zPkGVqU3yEjlMqYfV8Bcy0H4oqKY3w1LZVGrHot3XILYw03Ud37CpCu247Og9gB7JKHMmsVX/9tD16tPVEV0zPmxhOMcEVLBSqVxBvXVbPv9HgiKg6Eo3zvpfOsr7WwK97XkQnKNSqShCRJibJkKI4U01olusJzWeumwukNYTfpkGWZrsmTqMOrGXGI65C1E7NkGEjm7Pocwob31MQp9tTv4cyYh2hMZkO9IPb2ahO9Dl+iPFSn1mErs2WJ2MfTI/byJlBpFz4qcR417HCJELtNL6pTWmug3CwSRxVlFfQ7/Vn1dUiJ2PMl9ngCdMCvpr483WApIcVksgFuv1E8Zuomc/Vj1hjFsI1lRuyjBSbxCsWWRisA5ya8rC2PoTGkjP6qWB1/bE3bRylPVaQYbzDCTf/6PP/zcm/adkqU/sfb/zjt54sChdg9o7DtPXROdVNjqMPnN4qIPf47nGr7I2r8Iseg6LaxmMyYO5hzwEZW+J2sbW0hHI1x3KkTjVLRMEcviMTpFfEu6xs3VOPyh3ktXvb4+V91cGbMw6ffsj7nuLsRn5CMak2Z9d5E8nQBTUqtVeIY+SZQHZ4QlaYyeqd7mQxO0qDfyOmRIKqojZoKT8Yy3dRa9iOjR4jKUfbU76Er7jWTjNhNhCKxxOxdiHefzrTujYbFe51Kviq1+OwumNgLtxOAS4TYjRrxRq6pjtBeF0OOGDk54MUfjuaM2BW/mLxtBeJSzIBHomGG94zNoNwkMhB7zWbxR8skx0z1JeeeKsulZVLyOOISCbb5RI/5YE21mTKNirYqE1WaIOityReViL0iXRpIlWK6nd385XOfQ275e54ZTG/PPzRyCIvOwu1tt2PX2zk4fBGJ3doo8jIAO99Pl7OLRqNoXFpVaUqsOnr1G6muE4lHJRqe8AaJxuTC33NZBv8klooabt5QwwvK4tI7ztG+SewmHaviHurXr6lGrZJ4rmucX50Y4r4DfXxkbxs3bchNHso11hqzEHsRIvZqcxkmnZpeR37HcHhDVJp1iUEf2yq3c3LQRShgx2qdPUsZxErfXKahz+nj1eFXKVOXsaNmB92jbnQaFa1xS+K2eNXc2Rk6+6yIPbXUMRX2tiJIMYXbCcAlQuyjk6KUbu/g16iWTyNHzXz5yS4g3jLtGoD/fc+sIdMVhXqyx4m9d1rUvabCotcgSeDKFP2rVNB2g4jYU030Q17wOTDrbWLYhhKxF2mQ8FIjEbEvErFr1Cq+9u4dfPN9O5GC08JASUGC2FvT9rHoNUhqN98/939552Pv5OXRJ5BlNd2BX6aVNR4YPsBVtVehUWnYXbebAyMHCh+jOF+oVKL7s+kqfLZmel29WNXiBtVSacRclkwA17RcB8C4WzDx6HxvpsFpMQ/AUME917RyIRiPVD1jHO2b5IoWWyIaLzdquaLFxi9fG+IzD51kZ4uNT8UteXNhzDeGRtJg19szvr7QOnaIlzxWmQqWYo6PH6e8rJyrmkRzliZWjTeaeSi9JElxu2MfB0YOsKNmB2XqMjqHp1lbY0ajFrS4OoMslNFWIEG+M+QSe5uI2BfyuUttfCoAlwSxdw2JRJiHEC5vPxVllRzqFVp7i90Ix/8XTj8Jh76Xtp9VMQIrUGM/71HNithVKolyg3Z2VYyC9huFxDKW4qMdH4VnNlThDXuRtSYRqc1TivnbR05y67/t458f7+TVc45ZunE++PS+T/Pnz/45F6YvzOsaUlFoPfV8cPu2emEKFpwWdcAK6rcJC9/Ve9O2N+rU6MpPMBLs4i+u/AtqXV8gMPIOwtIkT/eKhpBBzyADngF21+8GYHf9bsZ8Y0V5T/LGu38M7/kJPVM9yMhowk1IkvDJ0ahVmHRq3IEIptqtGGIxxpyngZT3vFBiV+wEjHauW1OFLj4f1uMc4ty4l50t6dr5Detr6HP6UKskvvnenWjVc1PBqHeUamM1KinztlqVFo2kWVDyFITO3ptHyWM0JjPpC1Fp0nFs7Bg7qnewKW4wt7m6DWfQmXWUXYvdwPnJUXome3hD/RsAEhUxCqrMOix6TZoZWLWxmonARLrHj/J9nzkL194GYe/CAj3PWMF2AnCJEPup3gmMMRmXWsNExM/6lCRaU4UROn8pfjj6I6FnxSFJwggso3ySCSEvsqTGH9Ok1bArSLMVmIm2G8SjUlsN4BLEbjHXEZNj+KL+eC174VJMLCbz6LEhHN4g399/nru/+yo3f/WFgrzHg9EgT/U+xbP9z3LXo3fxtcNfyz2jcQ6MTgcoN2iL3pw0C9Fw0vJUgb4cProv4c+uQJIkygzTqNHx1lXv4/RQDHzrkcLV/Ljjx8iynJBddtcJYt9TJ8rxLqrOXrEKLHV0O8UAioC3joZyQ2IYuDLfU6rdTE00yvi0sCfOZ9ZpRih2AgY7kiRx4xViGPP+450A7EzpsgZ4y5Y6yg1avvqu7eI7lgfGfGOJxGkmSJKEQWtYkBQDojJmYNI/Z2AjeljAoA9w3nWeHTU72Fhn5W9u28A7twv7Z6UDdSZa7EaGg8JGYE/dHpzeEGPuYEJfV36fthmrh2ZLMzE5Rl/87wUkdfBMxA6zdfapfuh6POfvlsA87ATgEiB2WZap6P01FdEoUw3bcahVrFcFaLEbqbaUoff0w8hJEbl5RqHr12n7Vxh1BWnsUa0RkGZJMQDlRl32iN3aIDw4UuvZp0QEaLYIe1N3yB23FSg8Yj/v8OIORvirWzdw9O9u4XNv3SQ0wHNOIrEItzx4C+/51Xv49blfZ+2kPDd1jqgc5TO7P8MdbXfwg9d/wLt/9W7C0fl1Xo64FqeGfRaUJo5UjT0HNDoXZVIlr5wTZLZ3bQ1+xzWccpzitfHXODhyELvenhhI3Gxpps5Ud/Hr2YEuZxcWnYXRSUNavsii14iSzYrVVEflhH49Oh1AJZE2oSgv+OKTk4xCJvmdPVsBONHdI8zumtKJva3azPG/v4U3bco/KTfqG81J7CASqAuRYkBE7NGYnHWEnQJFgp1GNIPtqN6BSiXxkb3tbK0ROY0+d1/GfVvsRmL6HkxaM5sqN9E1IpLY6+vSze7aqs1ptezbqsXYvNfGU8bfZY3Y4wUAM4n9xX+Fn30gP4lmHnYCUCRilyTpzZIkdUuSdEaSpM8Usu+A08e7wo9hQsOQsRy/SkX11ABfevtW/vb2jUkiv/3foLwZDn8/bf8KU9IITJZlTgxMZXevC7kJq8SXa6YUA3Hr3lyyTvtN0PeKGFwN4s6r0mKxCHtTj1LyOA9iV4yZtjWXY9Fred+eFso0Kl4+O8GEf4IR7wi9rl4+8+JnePNDb+bX53496xg9U6IH4JqGa/j8tZ/nC9d9gX53P8fHjxd8PSBIZrFq2NOgDNkoy4/YJc0UmlgFL5+ZwKLX8KZNtYSnrsSstfCjjh9xcPggu+t2JzRlSRJDIA6NHCImzy1vPXRkgB+/0jvPXyYdXc4uNtg30O/0J5KXoNgPh0GtoUZjYixuqTHiClBtKUvovHkjJWIHMFtshFR6KmTRmGQqm93FmqsCZiZkWWbUN5o1carAoClCxK5Uxswhxzji3/vJyFlUkootVVsSrzVbRJljtoi93qZFY+5hnXUHapWajngHtFLqqKCtysSQK5BoZmq1tmLVWWcQ+5iQYMtmOKDaWoRv0ExiHzgimpfyuQHOw04AikDskiSpgW8DbwE2Ae+VJGlTvvufP/o0W1S9mM1NnHWJO2/V2GmuaTHyth2N0PkrUZVStQauvAfOvwATSYMlIcWE6HP4eP+9B7jzW/t55FiGenOAkJeAShB6Q4aIvcKYQ2MHuOoPhRfHA78HIZ8g+PImzHFCSpQ8zkOKea3fhUGrZk08E1+mUbOrtYJXzjoSDRFf3vtlvn3zt7GV2fj8q58nGkv3SzntPE2ZuowWi3Dmu6n5JjQqDS8OzraGzQcZu04z+IwvGMqQjTwj9ph6CqI2XuyZ4Oq2SnGTlnXsrb+Dpy88zZh/LKGvK9hTv4fJ4CQ9kz1zHv/bz5/hBzPKJ+eDSCzC6cnTtFnXMeEJ0VKZHrErJZs1hirGZWGNMZ/mJCBNY1cgmWuoklyJmQMLgSfswR/xz0nsRm0RIvZKJWmZ+ziKncB0ZIR6Uz16TfJ9M2qNohcmC7E/PfrfqLRT6Px7+PAPD/HFxztZVWmkekbX7erq9ASqSlKxrXrbDGKPd53OvFGqtYLcU4k95E26PuZjNzAPOwEoTsS+Gzgjy/I5WZZDwAPA23LtMDiVHE1VeepepmQz1bUbEta9laGAqEDxjIsIeeNbxY47PwAqDRz5QeJYdpOOXoePW7++j+N9U+g0quy2pCEvPvRYyjSJeuhUCH/3HMRe2Q7v+G8hDT32Z4LYbc2YtfFhG6lSTIGZ8NcGpnhjXQhNfCwgwNVtlUhPwzMAACAASURBVHSNuDnnFM01tcZa9jbt5b3r34837OW8K72U6vTkadpt7ahVQsc168xcWXNlRs/vuRCJxhh3B9MTpxNn4CvtwgOjmFA+4HlE7OFomIjkYtptYnDKz3VrqxJEuMN6O2pJ/O6Krq5A0dvn0tknvcIFcXx6tpdKobgwfYFgNEilVizJV9mTM2OtBm2ie7ba0kxQkph2D+Q9OWkWlCHW+qTkorXWsrdB5uM3rsm8TwH15jObk7LBqDEuOHlqN4mk5Vy17M64s6MjOEyTeba/TYulJV0Lj+Oxs4/x+IWHCDuu57dHqnltwMWf3LCGn37k6lmrmLYq8d1O1dl3VO/gzNSZhHGh8InJElUrlTEKhk+ICUswN7HP004AikPsjUDqbXEg/lwaJEn6iCRJhyVJOuz0hvirh04QdZxno+tF9lnvwGZIJkyr1Hro/jV0Pw7IsPEO8YKlFjbcIYyVwskkUygS4+r2Sp7+5BvZGvf5zoiQF0+sLKO+DsLofzoQzjmIgHW3wk1/Cyd/DoOHwdaSGGidiNijwYLMf8LRGK3DT/JNxx/Cwx9JPK9YjR4eEASuNIY8dlDclF7sO5J2nNOTp1lXsS7tueubrufM1BmGPcN5Xw/AhCdETJ6RxBs9BXJMPBYTgfwjdtEcIhPwi22vaa9K2NsGA1Zub7udVmtrYimuoM5UR4OpIeG7nQ3H+gVBuoMRfKGF+b53OUXJbllMkM4sKSa+Oqyxi/bz8cFD6aukSBBic7tYAkKK0ZeLQTEKTDXYZVfmqqbzL8KXVs2SNrNBWTXOSexa44KlGEmSWJ1HZYwixYz6hmiyzCb2ZkvzLI2929nNP77yj+yq3cXn3/hpvvW+nbz8mZv4y1vXZ3yflIapVJ19e41I6Cc+SzO7TlOh1LIrgd5gync2mHlGawLztBOAi5g8lWX5u7Is75JleVeNpYwHjwzwi/v/CxUyE+vfn/CLAahq3QvdT0LHo6KlvDapnbHrQyI6OfQ9kGU+dN1qHvzY1dx7zy4abMKVrWt4OnPNcsiDK6rLWBEDovtUlrMb/T95apib/vV5XFf+GWyKL0rKW2ZE7Bm6Tx/+Yzg1e6ACALEoU7/8G/5N/Q1UyCIajgpC2dZkw6hT0zk+gFalpaKsghFXgBc7ZOSogR8efSGx8pnwT+AIOGYR+3WNok66UDkmYw17PFmMK/sQ5nlB+YDnEbErN6hYxEadVU97tYkKow6tWmJkOsg/XP0PPHDHAxn14xpjDY6AY9bzqVC6NEHMHV0Iup3daFVaJqcqkKR0YleSp7IsU10rEp3Dw6/h8ocFwcgy/Od18NRn8zuZz5nQ1xOY4fCYgCzDbz8nApDHPyVIfg6MegWxZ+s6VVCM5CnEXR7njNhDWI0xHAFHRmJvsbYw5htLrCCmQ9P8xfN/gVVn5Stv/ArvunIVd2xrmOUlkwqjTkNDuZ5zKdeytWorKkmVlGO849nJ194mBosrUlkasc8R/M3TTgCKQ+yDQGp41BR/LitqrXr+6s3r8Y2cwSUbWb9hY8IvRiNpsK2/UxhpnX1GyDCpX9LVe6HxSvjNZ+E/rsHa+TN2NeiR3MMwcISbNK/hDwQym/UHPTgjujTzr1RkdXiM47mucc5NeLl3/3l423fgig/AxjtmROzx7jNFZ3eeg9f+F47fP/uA0QjcfzfVr/0H90VuZvKmL4uESlyD06pV7Gq10z89TI1RjPb6+eF+YrKKBsN6xkOn+f5+Ec0r2vFMYm8rb6PB1MBLg9mnQGVCxhr2SYXYc/55C0cgf2JX2trlcDnXrhFzcVUqiRqLnrHpAFq1FpPWlHHfCn0FzkDuHIFibwtkHHhcCDqdnayxreHVc1NsbSxPk/+sBi2RmIw/HKWmWgQug+OiNLLGUgZDRznrOofz5AP5uYX6nWn6OiAIwedIBAoJdP1KEMytXxTE87MPzNkhma8UU4zkKQidfWjKTzCSfcXi8IawWQQ5ZpNiAAbcA8iyzN+99HcMe4b56g1fTfO4mQvtNWZ6xpIkbNKaWGNbI4hdlueO2CEpxwweST43J7HPz04AikPsh4C1kiStliRJB9wN/HKunf7khjXcXOtjQtvAzhZbwi/GbrCjWvc7wkAHkvq6AkmCP3gSfve/AAke/RP4Yj18bSN87yZuPvJx3q9+OlG+lAo55GUyrKMhS8ONYiuQbY5qx7A45vf39zIV1cGd34TazRg0BtSSOlkVA8mIvSfuBT50bLbu3vcy9PyGJ+o+xld0H6NyU9yTZiCpA1/dVokn4qCirIpYTOanh/u5pr2SuzZejVo/xr889RodQ9OcnhQNLorTXvLtkri+6XpeHX6VUDR/O+GM9dRKxD5dZGJXxiLmIcUoFrexsI1r1yTlu1prGaPu3JN37Ho7k4HJrK9HojGO90+xq1UQ5Ngcx8sFWZbpdnaz1raeY31TCVlNgUWxH/ZHqIpHZBPxRF9duR6545d8qL6WL5lU6b0T2eBzgmFGktRcA8jpbqOxKDz7T8J9cPdH4b0PCHntgfflJJox3xi2Mhtl6txVUkbtwjV2EBF7TCZR8tgz6ub93zuQmAcL4PAEMZrEZyejFGMV8Wafu4/7Ou/j2f5n+cSVn2BHzY6CrmVDnYWeUU+aRLu9ejsnxk8Q8zlEx2+2qDqV2L0T4jvUdoN4bi5in46vjC1LQOyyLEeAPwWeAjqBn8my/HruvQSaGKN93WaMOk0iYq8yVAmtcPVeMZ2+6arZO2p0sP1u+OP98P5fwBs/A7d/Dd77U6LVG3mr+hU6h2e/aXLQgxd9VimmPEfEHonG6B51s3ddNZ5ghHtfSkY4kiRh0poySzHKtHLfBLgGeK57jE8/eEJIKAOHAPi+/wa2NpYjVbSK/QcOJ459dXslKu00UrScl85MMDDp5+7dLWyv3g7ImG0jfOKnx+h0dFNtqM7Y7n194/X4I36OjB6Z9Vo2jLgCaFRSmgNmMmLPXGkwbwSmRbWRZu7SyhHvCCaNlXK9ietTxrfVlevTvvSZUKGvYCo4lbXksXvUjS8U5S3x6TkLkWJGfaNMBifRxZqJxGSubU+PEJOeN2EMGgMWScNkUMhE9VY9Q92P4VSredloJHry53Of0J9BislkcXHip8Kp9KbPCj2+sh3e9UMY74Znv5D18GO+sTkrYiCePA37F2zfoLg8nhv34g1G+NhPjvDSmQl+05G0CXB6Q2j14kadKWJX8ixPnH+Crx75Kjc038AHNn2g4GtZV2shGImlaf47anbgCXs4OxovJc4WsVesAkkliH1QDNjOm9gHj4m/qXVWynJOFEVjl2X5cVmW18my3C7LcvZPRypisbQJ9IrGnlgive3bcM9jwiUtGyRJTCq58a/hqg/D+jej3vZurlCdYbR/RlmbLCOFvXjRZ02eJqx7M1TGnJvwEorE+N2dDdy+tZ4f7O9Ni+wtOouQYowpUkw4IPTLxl3iuaFjPHRkgJ8e7ueR44PQf4hY5f9n77zj5DrLe/99p8/slK2zvUqr1UqW1WVLsix3gw02NoZQzMXUBEzAQK5J4AZCMAkJ3IRACAQIcUyx8U1s3DC25IZ7l2RJq67tvU7Z3dmdmXP/eOdM2Sk7s1WSz/fz2c9KM2dnzs6e85zn/N7n+T2NvDGgyAYSIaBqmxzFF2FtuQNh8ODz53HPq+0U2IxcvbY0WrN7+foJjvX52N/XkiTDqGwt24pRZ8xJZ+/1TOJ2mGMOmIoSC+ienkTPnPkS8GRd6tjj76HaWcGbf30lJY7YhUBKMZkDcaGlkJASkhfgOKbD09z+zO384ZgcinD56lKMejEvKUbtOB0dLcGoF2ytSwy6jhkDQ9xGB8NimkI8VAbbaBmXlVBjOsHhU3tkeW0mxkeSpRjVu0T1MgkG4Km/l928zXGFaysulfJmhuHL2TQngczYg0pw3uMI6yMlj61Dfr56/1ucHvTjMBt48WRsjWTYPwWGYexGe8IanYrT5KTAXMBjrY/htrq5Y+cdOdXuq6g2A8fiijJkYgX7+yJJWDqN3WCWFr7Dp6QMI3RQt0s+N9viaddrMrGdwz4vX+eptwdCU+kDu7McSlIHqoysvQGAyq7EcWNMTyBQGFcsKZuTIH7YRrJkoTYwrCl38fnLG/FPBeVAgwh2o11KMQaTvOPwD0DbcxCcgItuk2WaPfs4Gjk4vveHIyidrzJcsJ5QWOH8qsiBWbVFjlWLLLaMh3wI3TSdg0b2HO7jxk1VmA16XGYX9a56PMoJIETPeGuSDKNiM9rYWrY1J529zzNJabxk5euD4KTsvg1Px4LFQjDpybo5qdffS5mtLGkmZ6nTgjcQxJ9hmlaBRUoVM3X2Lm8Xj7Y+ytOdeyi2m6kutFJiN89LilErYo6229lYU4DVlJigqCP+PGrJo62Efr2ezbZerCcfpcVkQhc5PV8wKdIrKR3BKZjypsjYI4HYNyBnrz50G4y1w+VfT/C4B+RFIIOnSbaBfSGMwEDePRfYjPzn8608sK+bL16xiqvWlvHSqSHCYYVwWGFkfJqgboAqR1XagF3trMYgDHx393dTBv9saCy1IwQciQvsNY4aCswF7B+KXAzTZewQK3nsfkOeP7ZCeYeaKWOfGJV3VlVb5rTPyxfYR1rl9xmBvchSlHr7bCmspzevme0TzyQOPI54pvixpDW1clnTSzGHezyYDDoaSvJoKnNwzbpy7ny+NWpnYDfZpcMjxLpPj++RHWkrrwB3M+GuNzg16GdrXQF6bztifJCjBulGt6E6Un9cHWmsicg06qKVxycny3xwW2ydel3xOlpGDuJ0jhIimDZjBynHnB47nbZhYyZJdgKqDFO7U35fyMqYHDP2sryypMdV/3J1bSAVhWYZ+Gbq7IMTUoPuGj/F5lrpgljitKScC5otR4aPUGWvpqV7KkmGgZgUEy15dNbSb9Cz2dILLQ/R4iphRcEKmgubeSHPmb6qCmI17EkZeyTYPHo7/GQnvHUvbP4YrLg8+TXs7rQX6+nQNMOTw7NWxADzHmgdT11xHj1jk1y8qoRbL13J9hVFjIxPc7TPy9iELEseDw+klGFUbtt0G9+/9PtRK4C5YDHqqSvKiyZlIOXX80vOZ7+3VT6QqXKlsEEma12vQ2VkULvZkTmwd0dkm7M2sEfmWeab83lv43u5tPrS+b90w7s4X3eKthNxUn8ksOvNeWlNrfQ6gdNiSNmkdLjbQ1OpI+qC94XLG/FPhaSkEtn/aCYYH9jrdoHRChUbCXe9SSgc5iPb67i5Up5Ej45WUea04FaDaMVG2YYckWPUwK5MO9lSW8BKd6xteX3JekYmRygokQunmQL7joodALzWK28d//XJ4/zT40fTbt83s1FGXTitla+zoIE9y4zdP+3HO+VNGdhLHXJf+zLIMekydjWwB0R3dBiF22Ges8Y+HZrmtb7XKDE1oiiwY2VysqLOblWblNzOGgb0enYqr0HPflqMepoLm9lZuZMDJj2+E3ti1gszidoJzFg8NTulxFKyGq75Hnz5KLz7+6lv7e2lkQqa5GNfHQKSjcZuNUYy9gWojDm/0kWFy8I/v389Op2ILkC/cHKIIX8ACOMJ9qVcOFXZWraV3dW7570vTaUOjvUlBuL1Jes5PTXCmF6ffFGNp7BBXnzHh+TfA2YP7J2vAyK2fY4sb2AXOun/gmzV/Zsdf8O6knXzfum8DTcBENgfl+VEvNhNtsy3Y/k2E2MzMnZFUTjc46E5zkdiVamDwjxT9I/d4Gqg3dNOIBSQJY89B+RVuvFK+QMVGzEERqkSA6wuc/AnZT10Cwv3636GvfKB2Gg0Ux6Urk3K2HevXMltVyQGbjULmTC/AIqOeld92t9LDYYjAZnd3fNqBw/uTz0uzhcI4gsEU5c6qoF9IStjsszY1YqY8rzypOfUC2OmjH22wK4zDbOmSmb+bsfcpZjnu59nNDCKObAZm0mfZMAF8VKMPNZKbG5CQlAReIMBvY7B0ARritawo2IHQRReNemkvUYqUtgJADKAf+pJ+OQe2Pap5EEQ8UQX/ZPtMLJtToKFGWit8tfvWsPeL++ODteuzLdSW2TjxZNDDPmmEAYfQWWKSnvui4u50lTmoHXIn6ACqNU1+53FmdcC1coYyCGwvyo9/S1zk4+WN7A7q6QmvcBU1jexT2nE3RZnlBUJ7HmOzAEkP+I9E0+/N8Cwf4o15Yk/u9Jt53ifvBNoKmwipIQ4MXpCniRqCd/KK+T3CjkpZ6P+NPXFeeQP7+cl10p05gH6eIpr7ruG7736PWmrULVV3raFQ9GT6scfuJSLGhNPzJX5K7EarEwoA4QCJUwH0/85rQYrBmHAE/Aw4p+ic2SCrtGJlF22aZuT7KVysLTRtsBSjFd6Ts+CGthTSzGzB3a1YmimFKNmpABWmwxsboeFkfFppoK5LxI/fOphCswFnGyrZGtdYcoGGLNBh1Ev8EzIjN2ml/s2YNDT4pZrJc2FzawvWY/VYOWF/BI4+N+p31CVYmZq7Lmg1kqrTTFxqMdgVhm7YeEydoNeh82UaF62vaGIl08PMeibQmeUF7RMGftC0VTmIKzAif5YB+raorXogX225PF7CaiB3WABd8RGy+JKH9iVSMVc5dxkGFjuwD5j7NlCodcJXrfvpmzieNQwTInMO7U7krOneFwpPNmjC6cVicGn0W3neL8PRVFoKpATaI4NH4tlP4UrZDkZgHsN0xjZldeJMRyA3rcIVMs/+De3/pCr667mrsN38Y0XviF19ikfDByhf7yfAnNByvphg87A2qK1AIQD5Rk79YQQOM1OPFMe3uqSF53pkJIyK+0bS1PDnl8js0BX1cJLMVlk7D1+2XWaKmO3mw3kmfQZpRiT3kSeMS9616IyODEIisy42rzSiE51tRzw5SbHeKe8PNX+FBdXXsmpgcmEWvt4hBA4Lcao374SlHeD/Xo9h0tXIhA0FTZh0pvYWraVF212OPVMdG5vAhNpMvZcUCtoUiyg9vuza06C2Hi8hdDYU7F9RRHeySDPHh9AmGSFTCaNfaFQ7XzjF1BtRhvNYSNvmjJk6xCbAla+XhqDQSRjT1MVM3xK/k3nqK/Dsgf2ukV7+b6qdwKg/PEf4Y27mDr4AACu/MyBPZUUozYmzbT0bHTbGZuYZsAXoNpRjdVg5ejI0VhgV2UYAIOZE6KGDfrT0L0PwkEGnIXohZ7rVl/Ety/6Nu9Z+R7e6HsDRb1Sd7wy63ADVY4JB8oS2p5T4TQlBnaAzpHkE7A32pwUdzEZaYuuh+CsXDgpJhySFR3ZdJ36e9EJHSW21BUIpS5Lxoz93lc7MCgO+vyJtgKnR3oIB8rRY5Z3XES6P4H+DK+Xir1te5kKT+HWbQekl006nFZjtCpmclIeW722QlosNmqdtdEO2h0VO2gL+ejUAz0pLJhVKWZeGfuM0sg4+sb7sOgtOE2z/40WUopJxfYGeaH8w6FedMZhBIIKe8WivFc8tYU2TAYdR2c0Pm6cCvIWgczNf0Yr1OyApmtij2WSYlTbgVQ9PFmyPIFdCcsDaBEDe3nNCp4PrUUc+C08+OeY99+FXzHjLKnO+HNyilLiH+lwt4eauOnyKo2l8mQ83udDr9PTmN8o65cdEakgLrCPTUzz+nQdtYFj0CEHPnTrdZTllWHQydvNNUVrGAmM0Gu2yZO087VZA/uGEqnzhQMVCUZFqXCanYwFxjjQOYrFKP/0qYYZJNkJhIIyQ1fvsFyVC5ex5zBko8ffQ4m1JPp5zaTUkT6wT4fCfOPBQwx7TOw5cpK/efAQv3uzi5t+/AL7ujvQhVzUOhqi1gzuyGJsrrXsD596mFpnLe1dxeTbjEnyXTzSL0YmET6/fL/OC2+lxddOc1FzdLvtFfIi8aLVktDjEGViWHZqm1JbKWRFtDQyWYrpH++nNK80qxrwaGBfACkmFe6IP9Do+DRmyyileaWY9Asv587EoNfR6LZztC/xHNvk9xBA4fBQ+h4AAD7+qCx7VskU2DtfBWMeuJtTP58FyxPYVe+LRQzsq8ucfHL6y7z6rsfhtoP84Zrn2BT4d4rdma/u+TYjYxPTUXMtkBl7qhO0sVRqa8cjC6irCldxdOQoysqr4KZfJJSVHevzckBpwBzySWfIgjq6A0MJ2YZ6Mh8ebpFX685XZq0f3l29m+9f+n1KjesSZjOmQs3YD3Z52L1KZr2pMva+sUkcFkNM3/R0SatRNWN3Vctb9mw8TGYjagDmyLwd0ogqlb6uUuo0Ry9KMznQOcbEdIj6QjeOvAC/frmN2367jz7vJHbbBO85fzXrS1dHh5Wodyu5BPZefy+v9r7KtQ3X8mrbCNvqCpPq7eOJd3jsHQuiBPPo8J2kx9/DmsLYSIN6Zz1leWW86CpO6EqOMh7xiZlDI0sUkw1Mjpg/SRyzJRfxRKtiFiljh5jrqcEysiQyjEpTmSMxY/cPstEn737f6H8jtxebLbBXbsq8IDsLyxPYQ5GTpSB9Fcd8WV3mYAILzw7nc8dzXj73uw4cdkc0GKfDZTUSVqRtK4A/EKR1yE9zisBeYjfjsho5HllQaSpowjvlpTcwDOe9N+FEO9rr5a1wZBGl7yBUbaXL25Wwot9U0IRe6Dk0dAiqtzI1eEzWD2dYtNIJHZfXXE5DsWNWNzynycno5BhdoxNsqS3E7TDTOZI6Y09cOI1YnxbESTEo4E1dVZMTORiA9fh7UurrKqUu2X2aqp395dNSfjmvrAKbZZLnvnIZ93z6QvZ86SImwx4q7KWszF/J8OQwQxNDFNnN6ERuUswjpx5BQeHi8qtoGxpnQ01m2U8O25DHWffoBEbyebHnRYCEjF0IwY6KHTxpVHiffz9f+eNX+I+3/iPWQTsxMj8ZRsVeknbxNOvAvoCLp+nY3iDlLUWf2tVxsWgqddDnCcTu6P/4PYoUqMsr582+N3N7MbNDNmgGZyQO0xNy3sM89HVYtsC++Bl7QZ6JMqeFHzx5gv94/jTv21LF41+8OElOSfq5SPepaitwpNeLosCaiuTAI4SILqCCrIwBpM4+g6O9XnpNtSiRKS9TFZvon+hPyNgtBgsN+Q20DLdAxUYGIoOPszmpVkRmM2by6JCBXQbSdVUuqgqsMmOfGIUXfxT1/u71zBiwodawRzP2yMm0EHJMltOT1NFsGTN2h4WpUDhlH8LLp4ZpdNspsxczHBjG7TBzYUMRY4ERFBSKrEXRzt3jo8fR6wRF9uxr2RVF4eFTD7OhZAPDY/J3SVXmGE/84mnX6AQ2fSH+aXlxXl24OmHbT637FDcXbqJ4OsC+3tf4/hvf54tPf5FgOCidGedgFJWEvTRprKOiKFn7xAAYdUZMOtOiLZ4CXNhQCGKKkG5syTN2kOcyQyfh1Z/Bxo+wqWI7bw68mdXYxShqIjMza+85IE3F5qGvw7JJMQF52zefVfwsuPb8crbVFfK7z+7k7288n8K82bW4mHWvvPioC6epAjtIOUYtgVIbhFSfkHiO9nppKCtAlEW8t4vrAJJqcNcUruHw0GGU0nX067MP7A0lefinQhmlA5fZxXjIB4RZW+GkqsBGx8g4tDwEj30V2p4HpBRTOrPrVOhiAT0a2OMWUINTsm09V6IZe+Zyx5HACIFQIGNgVy9GM+WYYCjMa63DXNBQSKGlkGA4GO0SHpyU5Y3F1uJYYI/q7NnXsr/c+zInRk/wroZ3caBT3p6fV5n5d3JaDdFyx66RCVwmKTFU2iuT2t+rHFX8xZYv8eO+AR5r/gzf2vktXu55mf/73Neh/1CsrHY+5CVn7CdHTzIdns6pVnwhxuNloshu5tLzpEy4lBm76hlztM8LT3xT2gJc+lU2ujcyFhjj1OipWV4hDlV6nFkZE+lfmU+pIyxnxl5QNz9NMAv++l1ruPfPtrO+OnPmFI/aDHHbPfv40VMneOHEIC6rMa3V70q3g2H/FEO+AHnGPKrsVUkZu6IoHOn1yCt+1TYwOeiyyIWumSdMc1Ezw5PD9OkU+uzyRM8qsEdGeGXS2WVVg0KdW4/DYqS60ErP6CSh0Ujm3f4yk9Mh+r2TiQ6Yo21SflFLtVS3OU9cxv78v8BPd6fvjkxHlhm7Wuo4m8YOybXsh3s8+KdCbKsvijYpqbXsQ5FRhCXWEoosRRSYCxIqYzJdKH/2x1N88Kcv4Q14+cbz36DWWct1K6/jQOco9cV5UYuKdDgsRiamQ3gnpxnyT1FilX/nNUVpRga718oegs5Xec/K93Bz88386vRD3G/Pg+brMr5XVthLk8od7z5yNyadiStqs79w2Azzn6I0G7dcLI+XpQzspU4zTouBiZMvyCFAOz8PjjI2u2XTUU46ezSwz8jYu14DV82878CWL2NfpBr2+XJ+pYvv3nQ+xXYz333sKI8e7KW53JG2IqDRHVlAjZNjVG90lV7PJJ7JIKvLHHDJX8Knn6ZrQp5AMwO7WpfeMtRCv0vKNNncBqtDd08Npq+McUZu/5rK5Z1AVYGNYFhhcjjiH9P+Ii09HsIKrI2/Q4kvdQS50GYtTJRiDv9O3kJ6ctTd1QvBLBp7pq5TlWglywz55OVTshzwwvrCpCalgXEpPRRb5dCOxoLGhMqYdIG9Y3ic7z5+lBdPDfGN5/6B3vFe7th5B1aDlQOdY6ybJVuHmK2A6kFSGTmZmwvTVEPoDVCxKZrVfXnLl7kgbORbxUXsm07vM581djdMjkZ137HAGA+deohrG66N2UGHQ8mDO2ZgNVgXVYoB6PTJY28ppRghBKtLHVzS9gN5Edz+ObkPjiqKrcVzC+yTMzL2oRPzqoZRWd6M/QxEpxO8b0s19/7Zdp7535fwF1et4otXpPdgiVbGxC2gtnvaE25F1aaGplKHzEyLV9Ll7cKgM1BiTazJXlWwCp3QcXj4MP15+ZjDCi797MONy50WLEZdxoxdCcksvKZEXqSqCuT/p4cjekoo9QAAIABJREFUAbrjFQ51yQCRICOMtidfiF2VMSlm+FRsDqq3l5zIMmPP1HWqojYVzZRiXj49RH1xHm6nJclWQLUTKIrM3G0saOTE6AnCShi308yQL5CyO/fbj7QgAH3eMfZ0PsBH13yUDe4N9Hvl9K6oW2cG1IlK6oze+nx5kY9fOE2iaovUYacnMXh6+F7HadxGO9955Tuzvt+sRGvZ5cXuvuP3MRGc4MPNH45t88Dn4Fc3ZnyZhZh7Ohud3k6sBmvK+QOLybttB2iabkG59Gtglue+EIKN7o25LaCmy9j9g3OacTqT5atjP0MDezy1RXl87rJGLmhI7zhZ5rRgNxs4EVfyqKBEy+Yg5uOsLr4AdPu6Kc8rRz+jpMlmtFHvrOfw0GH6jWbcoSBiML1Zl4pOJ6gvtmesZR8ck+9VGTkXqgtkzbHwdsk66CkvQyffpMAWJz0FA9JiOb+W6dA0/3Xov+RFy1kVa1KK9zDJYP2akoBXvrch88Wr19+LWW+mwFyQdhuzQU9hnilBigmFFV45PcwF9fKXnunwODAxgMvsitZCN+Y3MhGcoMvXhdthJqzIST3xvHBikD8c6uXTl5Rjr7wPs1LOrRtvBeCtiL6ejfyn+sUciazjXFW/i3/Y9Q9Rw7aUVG2Vtsm9B6DlIfLDYW5a+R4ODR2K+Q3Nlbha9mA4yN1H7mZr2dZoUQDhsBww3/a8rN5IgzpsYzHp9HZmtOtdLNaLE4QUQV994sVtc+lmuv3d0QRkVlItnobDmcfs5cDydZ4uYqnjUiKEkJ4xcRk7JC6gHu31Uuo0R/3eAbr8XWk75tYUraFlqIU+EcYdDMnypyxomGUAcGek4bLAIW+ly/MtCAGW8d7o4pu5+2XWVrhiJ8xoB6BAQS1PtD/B9177Hk91PBWxFYhIOEcejvlh+HLM2FU7gVlOUNWud7YT2e0wJwT2I70ePJNBtkUCe1RjD8Q09vi7ppUFKwG5gFqSokkpGArzzYcOU11oZdL+KIreg7f9JkIhedHc3zmGTsyQstKgSjFHer3oBFTm27mm4Rp0IsNpWRXrSqblQSg9j92rZJB5tjO3geVJRP1iBniq4yl6/D2J2Xr/ISnVhIMZj0mrcWHmnmai09e5pDKMSqkySC+FtI0m9nBsdEsvqDf6spRjUi2eqp/tHIZXz2QZA3vdsr31QhNf8lhpr8RutCfo7Ed6vTSVJZ7oM2vY41lTtIaBiQGOedtxK0LeemdBQ0keHSMTaY2rTvfLxwNhua9mg556uyKbpmouQHFUUOU7wNrKuH0dbZXf82t4sl3O3uzwdkgpZnJMln11vALnf0Au7HmT66AzEsjOsvfk6MmsKjPKXJYEKUbV19W7LovBgtVgjUoxAxMDURkGpLEayMBeYBfo7Yf51ZFfRFvGf/1yO0f7vNx2VRUPnLyfC0uuIjBeyUun5FXzQOcojW5HknlVKlQp5kiPhzKnBYM+i9PRUSYX1448DO0vQfN1rMxfSUVeBc90PjP7z2dClQB8ffzq8K+otFdySdUlsedb4wa1pGqUimA1WBe1KkZRFLp86c+fxcQ11Ue3UkTbjI7tVQWryDPmZa+zp5JiVGfNszdjF5CfubX/bKKx1M6AVzYuCCFYVbAqIWNvG/KzoiTW7j0ZnGRocijtgalqrL5pH6WWwuwz9pI8QmGF9uHUWXtLl8zUPVOxLGGdK7KtswqPewubxVHOK5+xcApMOcr5Y9cfgUhgd0aypVd+Cihy6Li9dO4ZewZax1o5MXqCiyovmvXlVpc5Odjl4ZsPHWIqGOaV08NUFVipjKvyiR9qPTgxmJCx5xnzqLRXcu/Re/n889djq76LRzp/wV2H72J8Ksg/7z3GzpVFDIgnmQhOcNu2T2I16nn66ACKovBW5xjrstDXQZY7AvinQlQWpJ7qlZLqrdD+IqDAmusRQnBx1cW81POStI2eK5FM8fBwC2/0v8EHV38wUSpsfU4mZM5KWb2RBpthYQZap2MkMMJEcGJZArt5vIcepZi2ocRzzKAzsKFkAy/1vJTdvFeDRU5VSwjskR6CFPbKiqLwpae/lPV+Lk9g1xuzGlx8ttAYGX4RX89+bOQYYSXMxFQI/1SIYnvs9+32y8qRdFJMc2EzAik5uB1VMrBnMWO0PkPJ44l+LwOeMHoMCYF9tS1yYDkrOGlZR7kYZoMzTqcfOgl6Ey/7O/BP+7HoLbR72mO17G/+Wsow7maZTeassc+esT/e9jgAV9ZemXE7gC9duYqP7azjP59v5X0/eYGXTg9xQX3iGkmBuYDhyWEURWFwYjA2jjHCBeUXMBGa4IqaKxhv/xg1li389MBP+dWrBxkdn+Yzl9Ry95G7uajyItYUN7FjRRHPHBuga3SCIf8U67MM7I64ZrnKNAPWU6I2rxSvArdsZNpdvZuJ4ASv9r6a/evMxGghYHbxN/3P4jA5uKHxhthz4bAM7HUXSU9x1agqBYu9eNrtk+fPkgf2cBjh6cJnKaVtKPn3e2f9O2nztGX3NxACzA6USQ+PnHpE3uGoBmz2ZCmmf7yfPW17st7VZQrsi2/as5SsTFHyOB4cp8vbFZn0AsX2OH3dKxcd02mENqONOlcdAO7CRul+qHZ/ZqAhWvKYHNj/ec9xbCYDLrMLT5yuV2+KWPjay3kxKBt0Kr0RB0FvH7z5S1hxGU90PEmeMY8ra6+k3dsupRiQ+9b8bnmg2ktzr4rJYnrS462Ps75kfcaKGBWTQcc33r2Wn9y8mVODfkbHp7mgIbFyotAqM3bftI9AKJAU2L+545s894Hn+PauO3Aq59Fo+BDT4Wl+fuhfWVPupDv0LMOTw3xs7ccA2N1UQtvQeHRwybpZOk5VHGZDdGmhYi6BfU1sIPXWsq1YDVae6ZifHPOPxQW0BD18e+e3E90cVX29bpcM7COtKYdyQKSOfXo8u8x1Dqiljkvh6piAfwBCU0zbK1MG9qvrrsZpcvLbo7/N7vXMDl4e7+Qvn/1LHj39aEYpZlaTsRksT2C3Zt8wdDZQmW/FatRHh240uORCYpu3TU5SBwrz4jJ2X+aMHWK1zKWlchp6NnKM02LE7TDzx2MDCSZmBzpHeeStHj65q4F8iyshY6/USUmiN5zPU8NFjAsbuo6X5JN7vg7BSUJXfYunOp5iV+UuVuSvYHhyGJ/ZIbtRAVa/W363l0Y7F6dCU9md2LNMT2rztHF05ChX1V41+2vF8Y7zynjkz3fx2UtWcM26xNp3NWNXB2zMDOxAdAHT7bAw7i/gsvKbmDC/zJUbJ7nr8F2sKVrD1jIZYC9ZJTOsnz97GqNeJEzayoROJ7CbpRyTkxRTsQne8R244DPRh8x6MxeWX8gfO/8454D60MmHuNcU5mNhO5fWzBhRqerrtTtjC7hpsnarwYqCwmRo7sPAM7FsGXukb8NQUE3rkD/pc7YYLNyw8gaebH8y2h+REbOTvQGZCLV52yJSjEjp+3N4+HDmRfUZLE9gX4DFgTMJnU6tjJGyhtoN1+HtYCga2OMydl8XJp0pZUBRUX3Wy6u2yxmoWersn7tsJS+cHOLfnj4Rfey7jx2lwGbkU7vqpcNjXMZeEh5gUHHSNhbmYK+fbsc6uSjX9iIcuAd2/Dn7Qz6GJ4e5vOZyapw18ncb7wV7mfxSx305SiHgwe8f4NJ7L+WR04+QkY5XZGWNO02nJURvP6+qyy2wA9QU2bj9HaujwVNF1dgHx2N2AulwO2X36UjXxRBycH/3t2jztPGxtR+LVujUFNmoL85j2D/F6jInZkP2rnyqd1FOUoxOBxd+BvISJabdVbvp9ndHO2dz4cTICb710rfYrLPz+VTDRU4/K/X1/Goo3yAv6vELqIoCe78JR/8QHbaxWAuoXd4uXGYXdtMsk4sWmkinta2kDu9kMKUn0fua3kdQCfI/xzMMH48QNtt5IiTvmDs8HVLGtBXKRrQZHB46TL0z+0rC5auKOceoLbJFLXBLrCWY9WY6vZ0M+2RgL5oR2CvsFRmvwDetuolfXP0LSl21Ukvtza4y5iMX1nL9hgr+755jPHt8gOdPDPLs8UFuvXQlDosxOkVJxTU9QK9SyB+PDzA5HSZQvg36D8NDn5cLpLu+zBPtT2DUGbmo8iJqHDKwt3vbYfMtsPt2GWhABnmgpfslPFMe9vfvT7+jaiDIK4EtH0+72eOtj3N+yflZyTDZUmApYCo8JX8HSGoSi6fEYeZkv4+nj3jYXnAzI4ERKu2VSS32qg1ytgunKo5IyWNOgT0Nu6p2AeRcHaMoCl997qvYDDa+m78Vw0zr3nBY1q7XRRavzXYoaU7M2Dtehuf+Ce77FLZpecwv1gJql7+LirwllmEgmrEXlMs78tahZMmz1lnLjood/L9j/08atGVgn8nAoAhh1pvlsegfSFvqeHjocHqriRRogX2BKHGYGYjUOwshqLJXRTJ2+VhRnMbe7eueVR80683RW33K1mWdsQsh+Psb17HK7eDzd7/Jtx4+TIXLws0Xys5RlylRirFM9NKjFPGHg/KW0LFKBgcGj8HV30Yx2nii/QkuLL8Qu8mecDfCJV+BrZ+IvXmkJf5IJKB3eDvS7+jJJ6DtObj49mgH30w6PB20DLfkLMPMhlrLrpakxpc7zsTtsOANBBFC8PVLPsr1K67ny1u+nDTsY3eTDOzZLpyqqBl7Thp7un21uVlTtCZnnf21vtdoGW7h85s+T4mrRspj8Q1GfQcj+vrFsceqIguoqhzxwg/lHM/QNLb9UmNerAXUbl/3knrERBnrBGMeVeUyyUilswO8v+n99I/3z3qB3SMCGBW4pv4aOrwdKP6BlBUx/eP9DE4MaoF9OXA7LPgCQcan5FW6ylFFp6+TIf8UJr0uQQ5QM/asKVsnuzxnjHRLh81k4Mc3byIYUjjS6+W2K1dhMUp5QJ2ipCK83XhMJbQPj2M26KhYu1O61jVcAmuu59jIMbp8XVxeI4eG5BnzKLIUycqYmUQaXFoiAbPNk2bBNxyW2Xp+jcz60/BY22NAdtUwuaC2oR8fOY5JZ8o48k0dkXf12lKqCvK446I7Uu7PxY0lfOfGdVy/ITfd12k1kG8zkmeeve49G3ZX7Wb/wP6oVUI2/Lrl1+Sb87mm/prUs09Vfb1uZ+yxyi0y2A+dlF9HHoFtn4bLvoY1kskvhhSjKIpMjJYlY+8AVxVVhXkIkT6w767aTamtlN8eSb+IqigKT4RH2TEVormomYngBIPj/RkXTtcWr816V7XAvkCURAKAmrVXO6rp9HYy5A1QmGeK6rHj0+PR2/msKZd6O33ZZe0ADSV2/u3mTXzkwlpu3Bh7L6fJiW/aRygcgqlxmBghYJMZSHO5E4PFDh97FG76TxCCR04/gkCwu3p39DVqnDVRGSOBiBRzxCef6/Z3Mx1K1iE5/DspLV36NTDE7mTCSphObyfdvm76x/t5vPVx1hWvW/DqB9WW4NjIsaj5Vzrqi2Wl0cd3ZtY39TrBB7bVRC+g2XJFcynv37JwPR3XNlwLSFfGbOj2dfNUx1O8t/G9WAyWWPdpvC9763OyU9wVlyWr6ypdr0svf71RBvYLPoOtUFZXjftzbFbLgqHJIQKhwNJXxID0RnJVYTHqKXdakmrZVQw6AzetuokXe15kx9072PGbHey4ewc/eOMH0W0ODR2iJxzgCp8/Jm9OjaYsdTw8JBdO1a72bFiYNEEjIbDXFuVR5ahiIjhB3/Rg1AoY5riiXxYJ7D37ZSadJbsaS9jVmJgBqNmpd8pLvnoH4KiEAThP7Titkift4aHD/PLQL3lH/TsSFhirHdW81P1S8hvaigjoDJwKDFOWV0avv5dOXyf1rrigGJqGJ++QC6br3pfw4784+Av+5Y1/SXjsy5u/nPXvmy2FkaoDz5SHOmddxm13ryrhmf99CbVF85gnmoEPbKtZ0NerddZyec3l3HPkHj5x3ieiC5npuOfoPQgEf9L0J/KBvFj3KSDdHNuelyWt8bib5VzO44/JbH39B6JByXbJX8ELf8nEqz+H+qsX8tej0xtxdVwuKSYyT6G2KC+p+zSeDzV/iPHpcabCUwgEHd4OfvbWzyiyFvHh5g+zt20vegSX+Dx4I46l7coUm1NIMerC6Wx/y3i0wL5AlNgTM3a1Rr1/ogd3Xswdsssna9hzyjhshVC4Qlar7PzCvPZTHeDgmfKQH1kMMhbIfV1bEdOHJ4OTfPXZr1JoKeRrF3wt4TVqHDU8OPEg49PjiQebTscJl5sgClfVXsVdh++i3dOeGNgP3Q/DJ+EDv0ma6Xho8BCltlJu3XAr0+FphBBcW3/tvH7fVMQbiWWqiAFZ8bRYQX2xuOW8W9jbvpf7jt/HzWtuTrvdRHCC/zn2P1xWcxnl9khJaNQvJiLFHH1USi6NM+QnnR4qNsLBSPVHxMIWwFYqg994x4vywjCP2Z0ziZYKL7UUMz0pG4gidy21RTb2tqS/I3GanHxpS6xTNBQO8aWnv8Q/vPIPlOeVs7d9L1ttleSH27Ab7BiEng6jIaUUc2joENvLt+e0u5oUs0BEM3ZfTIoBGJ3uSaqIgTnU4NbugLYXsupAzYSasY8FxqLe6a4yubAa7yH+L2/8CyfHTvK3O/82aZqPWvKoNorE05InX//qOpmpJUk2r/1CdqquemfSz7Z6WmkubOaGxht4f9P7ed+q9+WUpWSLzWjDErFCni2wn42sL1nPJvcm7jp8F9PhFFJYhN+f+j2eKQ8fWv2h2IPRjD0S2F/4gVwLaUpxgY3c2dF4NZTEZAL1bzaBkjRqb77M1rW9aKhOptHAnsegbwpfIFb58uuX2/inx1M7sep1er5z8XdYW7SWv3jmL2jztHFlgdTMDdMTVFiKaTMYkqpi5rJwClpgXzAK80zoRCxjVw88X6gvoTmp3duO1WClyJK+EiMltTtl5jTQMq/9VIdteKY80YP1ki3rufNjW6Me7C/1vMSvWn7FB1d/kJ2VO5NeQ9UEU1W9HDGbcShwXvF5OIyOxAXU/hbpcbL5lliJZIRQOES7pz3acbvYqJUxxbZzL7ADfPy8j9Pj7+Gx1sdSPq8oCr8+8muaCprYXLo59oTBBNYCmZ22vyzLGLd/LmVtNXWRCqoZd5HRgdZCxALiAtHp7aTQUrgoF/yMzAjsdUXy/VWdPRgK8897jvPz506n9O8H+bn88PIf4ra5EQguK5GOkAS8VJsL6DAakzJ2deF0SQO7EOK7QogjQogDQoj7hRDnVktpDqjDj9XAbjFYcFvdhHSDCaWOBwcPSi+YXH2kayMe3W0vzGs/1YxdBvZusBZistq5pElmCpPBSb7+/Nepc9bxxc1fTPka0ZJHT3JgbxEhmqbD6IROLrLGV8+8fqe0k9jw4aSf6/Z3MxWemlXzXiiigf0czNhB1rQ3uBq48+CdKTtR7z5yN8dHjvOh5g8lH4t5bqmxv/ADGeQ3ppFzVl4Btx1MrJaB6N3QhE6Ap2dBfh+V5auIidydRgJ7TTSwS539xVNDDPoCjE+Fop5RqSi2FnPnO+7kZ1f9jGL1riPgpUZvo91oQLElJnyHhw4jEEnDzWdjvhn7HuA8RVHOB44BfzXP1zurccfVsgO4bRUI03BUipkKTdEy1BLtKs2JglpwVUcHTs+VaGAPRAK7M1ES+s2R39Dj7+Hr278ezbxm4jK7yDfnJ8ksoXCIY2E/qyf8EAomVs9MjcP+u+VszhQLRGpmv9QZe6bmpLMZndBxy9pbODpylD+0/iHhuYdPPczfv/L3XFJ9CdetSDEr1e6GrjfkoujWT4IpzRqDSO3SqtfpseotjAtd7qMSZ6Hb302lY+ldHaOBPXK+qOsuapPSA/u6MejkBXJ/x2jGlyrLK+OC8gsShm3UYsSv0zFsTJyTe3joMA2uhpzvUOYV2BVFeVxRFFVkeglYhqXqM4eSGcOPC03l6IzDUTuBo8NHmQpPzS2wQ0xnn4e5UpIU44xlP2OBMX7+1s+5uOriWHNUGmocySWPrZ5WJpUQzVNTMD5IjaOGHn+P9DI/dL/0b9/ysZSv1zrWCrBkGbs6SelczdhBlj6uzF/J7X+8ndv/eDv94/083fE0/+e5/8O2sm18b/f3khqtABnYPV3y7mrbp+f03lajjXG9YUGlmLASzqq5b1EY65B3MhFXWrvZQLHdRPvQOJPTIR472Mt1GypwWgzs68wc2KPEDduojiyddUwm9qrk2nGqspAa+8eBR9M9KYT4tBDiNSHEawMDC7ugcqZQYk/M2O36UnRGD45I4ntgUNoCnF88j8Du65MNIXPErDdj0Vsii6eJgf0/3voPfFM+vrBp9sqbamd1khTTMiz1/9WBKfD2UuuslbXpvk54/T+lNUJtsmYP8qLgMDqWbIal+j7ncmA36U3cfe3d/Nn6P+OJtid49/3v5i+e+QtWF67mB5f9ALM+jXW2WhkTV8KYK1aDlXGTbUEz9oHxAabD08syOUmtYY+ntiiP1iE/Tx/txxsIcsPGStZX58+asUeJG7ZRMyXjRnyyNDA+wMDEwOIEdiHEXiHEwRRf18dt8zUgCPw63esoivJTRVG2KIqypaTk3Lz9LXGYGfQFos6KFuTvOS1kF+CBgQOU2kopzSud2xuoQXEB5BjP5AiMD0VvLXv9vfy65de8e8W7WVWQfni3SkI2HuHI0BHMOiMN09Pg64tWz7S3PQudr8pF0zRrC61jrdS56pZshmVjQSNFlqKMdgLnAhaDhVs33Mrvrv8d28q30VTQxI+v+DF5xgwlnPk10uRrx5/P+X1tRhsTJkvKwH7v0Xt58OSDOb/mnEqFF4qxzhSB3Ubb0DgP7Oum2G5me0MR66vyOdLrZXI6NPtrxgX2Sr8HnULCmtShoUNA7gunkEUdu6IoV2R6XghxC/Au4HJlsQyYzxJKHGaCYYXRiWkK80zoQzIb9Ct9wHkcGDgwdxkGoGilXDVvewE2f3TOL+M0O/Gog48jGfu/7fs3FBRu3XBrVq9R7ahGQaHT1xm1KW4ZbqHRWY+BkzJjr7kAgLZjD0mbgvUfTPt6pz2nuaDsgjn/Trly3YrruLbh2tRSxDlItbOaH172w+w23nyLbIQrbpzz+9kMNsb1JhhOlGIUReFH+34EwLX11yYNc8/EnEuF54uiyMC+MjEU1hbmcd8bXQz5+/nQthoMeh3rq/MJhRUOdY+xuXaWu09THiAg4MU4PkS5zZiQsf/+9O9xGB1LL8UIId4B3A5cpyjK4k6vPQuYaSsQnpbZ4NBkD0MTQ3T6Oucuw4DMdlWdfR44TU48E8OR/1RwavQUD5x8gA+s/kDW2ZBap6/KMYqi0DLcwmrVz8LXT74lH6fJSfvAIWh6p2y0SsH49Dj94/1LtnAK0izt7RLUc8ZolZ2l80AGdr3M2OPyvU5vJ8OTwwxPDvN6X/opTKlQm5PK88pn2XKBmRiBaX9suEyEumK5oDkVDHP9BnneqCZw+zrGmBUh5AJqwAv+AWoM9uj5NDQxxJ62PVy38jpp9ZAj89XY/xVwAHuEEPuEED+Z5+ud1czsPvX5zRA20enr5K1B6fMyr4wdoPYiGGuH0RReLVkijcAiOqCriic7niSshPn4eentc2cSlVm8MV8Y75SX5uLzZIlcZPZpjbmQdjGd3JIeR7QiZokWTjUWH6vBKuvYQwEZGCPsG5DTuQQiOvJQJRAK8Nm9n02q4lHp8nVRbC2eU6CbFzNq2FXUypiaQhsbqmWlt9tpocJlyU1nnxyTgd1cED2f7j9xP8FwkPevev+cdnleKYuiKCvn8/PnGm6nPOAGfHJyzMj4NEalhE5vJwcMBzAIQ3RQ9ZyJ1rO/KLXQOeA0OTkSjBgYOcp5c/+b1Lvqc1pILDAXYDfa2dO2B8+Uh7YxGZybC5ulGVhkRF7N9DT7jCZoTG+92+ppBZau1FFj8bEZbYyLSKbu6Yrere3r34fdaGd7xXb2tO3hr7b9VVSOefDkgzzb9Syv973OuuJ1SZJLt697fjLM+LDspbjws2DM4eIwo4Zdpb4oD4NO8J6NlQlrQ+ur89mfS2XMWAcoIaptZXgGTjE8Ocx/H/tvtpZtpSG/Ifv9jEPrPF1AZkoxQ/4pbMJNh7eDA4MHWFW4Km1teNa410jf67bn5vwSTpMTT2gSLC7CJhv7+vexoWRDTq8hhGBT6Sbe7H+Tn+z/CXvb91LnrGNV4Srpy+7rA0WhdqSLHoOegDH98PLWsVYEItrRqnH2YzPYmAhHFhDjFlD3Dexjfcl63lH3jgQ5JhQOcefBO2lwNUjv++e/TlhJtM/o9HXOb+H06O/hiW/CM9/J7eeigT2xZt9lM/Lg5y7i1ktXJDy+vjqftqFxRvxTzIrZAcOngFhH9z1H7qHL18X7m+aWrYMW2BeUPJMeq1FPv0cG9mH/FC5jKV2+Lg4OHmRd8br5v4lOBzU74NTTc/aNcZqdjCshpp0VnB47jWfKw0b3xpxf54eX/ZDXb36dA//rAG985A0euuEhWUKnzj7tPUCNdxCFmCtfKk57TlOeV770t9gai4bL7MIT9OONsxXwTfk4PnKc9e717KrahdVgjVoePNnxJO3edj674bPcvvV2Xul9JcF6OBgO0ufvm1+po+pY+fy/QGcO+v5Yh1z8T2E/saYieRTi+sgw86yydrMj+vnURLLzOw/dSZGliMurL89+H2egBfYFRAghJylFjMCGfAGKzBUEQgH8037Wl6xfmDc670apsbc+O6cfd5nkAo/XVcWb/W8CsMGdW8YOsrvRpDcllyjaS8HbB4cfpDYos7a0QzeIlTpqnDvsrt5NUAmx154XzdgPDB5AQWFDyQasBisXV13M3va9BMNBfvHWL6hx1HBFzRXcsPIGdlXu4vuvf582TxuKotDp7SSoBOeXsfsHwWAFRzn87jPSsTEbxiL9HrrswuW6KhdCwP5sFlDVkkeDvEoRAAAWw0lEQVSgqqgZgWAiOMGNjTdi1Bsz/GBmtMC+wKgj8ianQ/inQpTnxTTBeS+cqjRfB5Z82fQzB5xGOYpurLCGff37KDAXLOzCpaNMLprtv5uacmkwlW5MnqIotHnatIXTc4zzi8+n2lHNI878aGDf378fndBF71yvrrua4clhfrz/xxwcOshH134UvU6PEIK/2fE3GPVG3vvge9n0y028+3dy8V2txpoTvn55bF73Axg8mp0kE/DJ0YCu7O8U7GYDjW579hm7+k9nJaV5peiEjvetel/Spm91ZnGhiKDVey0wJXYzJwd8DEf0tRpHNQzIW9MF05CNFtjwIXjlZ+AbAHtuDV/OKVmZ6nGWs6//Gda71y9sY5DauejpwrXzNlyn70qbsQ9MDDAeHNcy9nMMIQTX1F/DTz3/Tv9YO26kvt6Y34jdJBOLiyovwmqw8tMDP6XIUsT1K6M9j7htbn50+Y/4/anfYzfZsRvtlNhK2FK6Ze475e+XnbQrr4CNH5GSTPO7Y9OgZtL9Jvz3J6QGHuc3nw3rq/J58kg/iqJkPrdUvxihA1shOyp2EAqHYv74EYKhMO/5t+wbE7WMfYFRpZghnwzs9flVCATnF5+/sMFz8y0Qnob9v8n5R50+6UfRZjLT5mmbk76eEXtcZ+3qa6l11KYN7EvtEaOxdFzbcC2KgEcnuwiFQ+wf2J8g+VkNVnZXyZGLN6+5OcniYKN7I1+78Gt8YdMX+MS6T3DdiutyamhKwjcQs8W9+tvyrvelHydvpyhyOPfPr4TgJNzyMGz6SE5vtb46nyH/FJ0jE5k3VDN2WxHo9Hxzxze546I7kjbrGZtMawecCi2wLzBuh5nR8Wl6PVK/K3Xm8eHmD6e8tZoXJU1yEfX1O3NeRHV55SLSM17pObPggd0hZ59SuRlclax3r+e1vtc4MHAgaVO11DFhypLGOUG9q541BheP6CY5MXoi5TrTB1d/kE3uTfOqAMkaf1xgt7hkCe6JJ+SUp3han4PH/w+suhr+7Dmouyjnt2qIzMrtGs0ysKeYnBRPx0hu/Z9aYF9g1JLHY31eAArzzHxl21e4tObShX+zzbfI28QcF1GdI1LvfqH3FYw645xaljO/QYWchxmZafqZ9Z/BbXPztee+xmQwccHq9NhprAYrbtvczKY0zmzeld9Mi8nA7478FkhepN9Uuon/eud/Re2kF41QUHojxZuaNV4JE8PSojiew7+Ti6w3/ixtt/RsOK1y4XNsIv0EKyAusGfuIekcnuUCMQMtsC8wamBv6fEAJAzZWHDWqIuod+b0Y85I3axv2sfaorXpXf7miikPvrAftv0pAA6Tg7/d8be0elr54ZuJfiWtnlZqHDXohHYonou8s3wnOkXh7hP/Q5GlaHmcGUEGdZTEzHjFZVLbPh7XARsOQ8vD0HgFmOY+pcmVc2DPnNh0joyjy0HJ1c6mBUYN7Ed6vRj1Aod5EdenjVZprNXykNQPs0FRMA4cx4rUKhdchlGxlySUh22v2M6fNP0Jvzz8S17vex3PlId7j97LgYED2sLpOUxx0SoumJwkpITZ4N6wZO6dSfgjpnfxGbutEKq2wYk9sce6XpN2GM3XMx9cNhnYPbMFdkvkTmVWKWaCclf2zY1aYF9g1MB+etBPYV6KGu+FZuPNchG1JUsb1LFOmPbjjHTAzqV+fa58afOXqHJU8YWnvsBl917Gt176Fm6bm4+umbtTpcYZjrOCa31SH861u3lBUYdqzwygjVfK6hd1eHfLg6Azwqr0FhjZYDcZ0IlsMnY1sM8ixYyMU1WgBfZloygyuDoUVqL/XlRK10LhCpm1Z8OgnKLuMssmpaUM7Dajjb+76O8oMBdww8obuOdd93DfdfexrmQBOnI1zkwc5VzlH+dDjiauabhm+fZDvaOdKXk0Xim/n9grq2EOPygtiy2ueb2dTidwWo05SDGzZOzDE1QVZC8NaXXsC4zJoKPAZmRkfHpx9XUVIWQt7ov/Kk2OZlvsGTgGQIHNTa3esGQTi1Q2uDfw0A1ZXoQ0zn4MZqy2Yv7KWAnLuUAelWJmBNCy86Vp3fHHofQ8GG2DXV9ekLd0ZRPYi5vg0q9ldD8NBEP0eSepLtQy9mXF7ZCeJ+qs00Wn+ToIB+HYY7NvO3gUrAV8cdtX+PZF3178fdPQcFbMbUTevt/A3m8uzD74+qXfi3lG9Y0QcqH05JNyLq/QweprF+QtswrsOh3svj1jQtY9OomikFPGrgX2RUDV2ZcssFdukiPuspFjBo5BcRNri9cunHeNhkYmnJW5B3ZFgaf+Ht781cLsg39Qyh2p1rwar5Ke6C//uxw/OYvenS1ZBfYs6IzUsFdrGvvyogb2YvsSaOwQk2NOPiG9LTIxeBRKZp9pqqGxYDjKY8MqsqXzNTlQZnI0YQLTnPH3p7feaLgEdAY5JSmDJJIrWWnsWdARqWGvLtQy9mVlyTN2kAdkcFIuAqXDPyjreYublm6/NDScFZHxcjk02Ry6T34PTeX2c+nw9aevFbe4oGa7/PcCyTAgM/ZZyx2RlTOZxkV3jIxj1AtKndnbWmuBfRFQR+QtaWCv2S79ojPJMQOyIoYSLbBrLCHOiMNptnJMOAyHfgci4gszmeU0okz4ZzHL2/UluYiZg4vjbKhSTKag3TkyztY79nLTT17kjfaRNNtMUJFvRZ9Dh5IW2BcBNWMvWsrArtPD6mvkAmowkHqbSKkjxZoUo7GEOCMe6qkC+0gr7Pl6ojd6x0vg7ZYD0CFhZuqcUJREn5hUrLhMLmIuIC6rkemQwsR0KO02r7WOMBUKc7zPy43/9gKf+80bdM/wl+kYzq2GHbTAvihc0lTCJy6qZ13V/Gphc6b5OpjywqlnUj8/cAyMtqQRXxoai4qaBacawH7wPmmf+8TfJj5miHRVA0zMM2OfGJFVY7O07S802dgK7OsYxWrU8+xXLuPzlzeyt6WP2+7Zl7BN58gE1TlUxIAW2BeFfJuJv37XmqSRWYtO/cWynGtfmkqCwaNQtDLrSTAaGguCq1rKKiOnk5+L+Bbx0o9iTouHH5Cdn66IhDNfKUbtOrWfeYF9f+co6ypduKxGvnTlKv704hW82jYcnecwMRVi0BfQMva3NQYzXPgZeWK0phh2PXBM09c1lh6DCfKrYehk8nPDp6F8PZSsluPqDj8gK1jW3gjWArnNfKUY1S5glu7OhSYa2MdTB/apYJhD3R7WV8fu7C9d7UZR4Nnj8mLUNRopdcyhIga0wH7usfM2mSH9/nZpVari6QFPpxbYNZaHwhWx7Dye4VPgXgvv/bkM4Pf/qbR8brxKOpfC/KWYdD4xi8xsGfvRXi9TwTDrq/Ojj51f6aIoz8RTR+TFSC111DL2tzsmG1z9d9B/CF77hXzM1w93XS/19VXvXN7903h7Utggg3h8hcjUuFwkLWyAsnVw+TdkeePqa+RxbHYCYnYpZqwT9t2dvt79DJVi1Jmo66tigV2nE+xeVcIzxwYIhZW45qTcMnbNK+ZcpPndsuniqTugfhf8v1tgrAM+dC+UnbfMO6fxtqRoBQQ8so9C7exUNfeiBvn9ws9Kp9KmiFmYTgfW/NmlmFf/A577JxnAd34++Xlfv9T4rUvrizTbsI39HaMU5ZmSsvFLVru5780u9neO0jEygcmgy7nZUcvYz0WEgHf+I0z54Se7ZDXCh+6VQV5DYzkojATveJ1dlWbU53Q6uOiLiXKhJX92KUatttnzdTjy++Tn/f3yYrLERQMOswEh0nuy7+8cZX11fpK19+7GEnQCnj7SHy111OUyZQMtsJ+7lDTBjs+D3qQFdY3lp3CF/B6vs6v/Lsgw79aan50UU7kFKjbC/3wSeg8mPq/6xCwxOp3AaUltK+ALBDne70uQYVRcNiObawt46ujAnEodQQvs5zaXfx3+9wktqGssP/k10jlxZmC3FcngnQ5rwexSzFgHFDfCB34j7QHu/kDiRDFf/7IEdkhvBPZW5xiKQkJFTDyXNLl5q2uM4/3enBdOQQvs5zZCzGtuo4bGgmEwyeA+PEOKUWWYdMwmxYSmwdsjK8Gc5fDBu6Xh2Cv/HtvG37/kC6cq6QJ7qoXTeC5tkvs7OR3OudQRtMCuoaGxVKiVMSrDp2cP7LNJMd4eUMKx7taKDVB3kexeVRT55ZvFTmARSRvYO0apKbRRkMZ2pLncQalTLphqGbuGhsaZS+EKGIqUPE5PSm181sBeIDP2dKWMox3ye36cTcZ575V3Br0HZAFBcOKMDOzx9eszEUJEs/Zl09iFEF8WQihCiIVxqNfQ0Dj3KGyAwJgc4TjaBijZSTFKCALe1M+Pdcrv8f5HzddJf/WD98WNxFseKUZ6sgcTHuv3TtI9Nsn6Wbyk3r+1mo01+TSW2nN+33kHdiFENXAVkMLhR0NDQyNCkVoZczJW9qhWy6RDXVhNJ8eMRcJOvN2urVD2cRy6L85OYPk0ds8M694DHWMAbMiQsQNsqing/s/uxGbKvd1oITL2fwZuBxZgzImGhsY5i5qdD5+Kq2HPUOoIcX4x6QJ7p5xDYJyhQ6+9Uda3H/uD/H8mL/ZFxGU1MhUKMzkdjj52oGsMvU6wtmLx3F/nFdiFENcDXYqi7M9i208LIV4TQrw2MDAw2+YaGhrnGvm1suRx6KQM7Jb8jEOcgTi/mDQlj2OdqYdjrL5W9nC8fqf8/zJq7JDYfXpywEd1gRWrafHcX2fN8YUQe4GyFE99DfgqUoaZFUVRfgr8FGDLli1adq+h8XbDYJJa+PApaS0wm74Os0sxox2pZ/ha82HlFXA00ol6BgT2MpccbXd6wE9dcd6ivu+sGbuiKFcoinLezC/gFFAP7BdCtAJVwBtCiFQXAQ0NDQ2psw+fzK6GHTI7PCpKJGNPMzhm7Y3yu7UA9Ma57e88mZmxK4pC65CfuqJlDuzpUBTlLUVR3Iqi1CmKUgd0ApsUReldsL3T0NA4tyhsgMETsls0q4w9gyf7xAhM+9MH9qZ3gMGybAunkBzYB7wBxqdCNJQsbmDX3B01NDSWjsIVcnwjZBfYTXmydDGVFDMWqWFPN4Da7ICtn5QNTMvEzMB+etAPsOgZ+4IF9kjWrqGhoZGe+GCeTWAXIr2tQLSGPU1gB7j627nt3wKTLrDXL7fGrqGhobFgFK1I/e9MWAtSZ+zRrtOa+e/XIuGwSOvesXE5w/T0kB+TXkdFfu42AbmgSTEaGhpLh+ryaLJLZ8dsSDdsY6wDDNbsX2cZ0OkEDrMhmrG3DvqpKbKhz9FfPVe0wK6hobF0GMxSOrEWSJklGyz5sfF28Yx1yNfK9nWWCZfNGBfYxxddXwctsGtoaCw12/5ULopmi7UAho4nP56uOekMQzUCC4dlqePFqxbfUksL7BoaGkvLjs/ltn06KWa0Q5Y0nuGogb3HM0kgGKa+OHdTr1zRFk81NDTObCz5MOmBcFzZ4vSkdG5MV8N+BqEG9la11LF48YffaIFdQ0PjzMZaACjS8lfF0yW/nzVSTHDJSh1BC+waGhpnOtYURmDR5qQzP2N3Rqx7Tw/6sRr1lDosi/6eWmDX0NA4s0nlF5NNc9IZgmrde6TXQ22RDd0ilzqCFtg1NDTOdFS/mPgmpdEOQICzcll2KRfU7tMDHWNLIsOAFtg1NDTOdFJKMZ3gKJNWwGc4amD3BoKLbterogV2DQ2NM5uUUkzHWaGvQyyww9IsnIIW2DU0NM50Ug3bGDl9VujroAV2DQ0NjWSMVumrrmbsgyfkPNOa7cu7X1kSH9iXwk4AtMCuoaFxNmCJ6z499qj8fhZ0nUIssDvMBortS7MmoAV2DQ2NM594696jfwD32jParjceh0UG9rriPMQSGZZpgV1DQ+PMxxoZtjE+DO0vQtM7l3uPskavEzgthiWriAHNBExDQ+NswJIvSxxP7AUldFYFdoC/ftcamsocS/Z+WmDX0NA487HmQ99BOPqoHE5dsWm59ygn3rdlaUszNSlGQ0PjzMdaAONDMmNfdRXotNCVCS1j19DQOPOx5MP0uPx30zXLuy9nAdplT0ND48xHbVLSm6HhkuXck7MCLbBraGic+ahGYA27cxur9zZFC+waGhpnPqpfzKqzoylpudECu4aGxplP7Xa48FZYd9Ny78lZgbZ4qqGhceZjdsA7/m659+KsQcvYNTQ0NM4xtMCuoaGhcY6hBXYNDQ2NcwwtsGtoaGicY2iBXUNDQ+McQwvsGhoaGucYWmDX0NDQOMfQAruGhobGOYZQFGXp31QIL3B0yd/4zKUYGFzunThD0D6LRLTPI4b2WUCtoigls220XJ2nRxVF2bJM733GIYR4Tfs8JNpnkYj2ecTQPovs0aQYDQ0NjXMMLbBraGhonGMsV2D/6TK975mK9nnE0D6LRLTPI4b2WWTJsiyeamhoaGgsHpoUo6GhoXGOsSyBXQjxUSHE8cjXR5djH5YTIcQGIcSLQohDQogDQog/iXuuXgjxshDihBDit0II03Lu61IhhHAKITqFEP8a99hmIcRbkc/iB0IIsZz7uFQIIWqEEI8LIVqEEIeFEHWRx9+ux8Y/Rs6Vlvjj4O16fGTDkgd2IUQh8A3gAmAb8A0hRMFS78cyMw78L0VR1gLvAL4vhIjM/uIfgH9WFGUlMAJ8Ypn2can5FvDHGY/9GPgU0Bj5ervMRbsL+K6iKM3Ic6Q/8vjb7tgQQuwAdgLnA+cBW4HdkaffrsfHrCxqYBdCbI1kpBYhRJ4Q4hBwK7BHUZRhRVFGgD2cw3+QNJ+BSVGU4wCKonQjT9ySSMZxGfDfkR//L+A9y7Lji0Cqz0IIcZ4QYjNQCjwet2054FQU5SVFLgTdxTn0WUDaz+N8wKAoyh4ARVF8iqKMn+vHBqQ9V/SABTABZsAI9L0djo/5sKgNSoqivCqEeBC4A7ACvwKmgY64zTqBysXcj+Uk1WegKMpB9XkhxDbkQXsSKAJGFUUJRp4+pz6bNMfDYeBJ4GbgirjNK5G/v8o59VlA2s+jARgVQtwH1AN7gb8ECjiHjw1Ie648K4R4CugBBPCviqK0CCG2cI4fH/NhKTpP/xZ4FZgEPg98cQne80xj5mcARLPSXwIfVRQl/DaRCGd+Fp8Ffq8oSufb5PefyczP4wZgF7ARaAd+C9wCPLBM+7fUJHweQoiVQDNQFXl+jxBiFzCxTPt3VrAUGnsRYAccyFuqLqA67vmqyGPnMjM/A4T4/+3cr0tDYRTG8e9BxSbaRcS/QMSgSVBcF2zC/JGNBkHsBjFZbCKYRLSImKz+KENFi4iIYLKI/Rjed7A5XFDm4NznAy9sd3ew+3Du2eV9d2c9wAmw5u4Xeb93oNfMql+4EbP5nsU4sGxmz8AmUDazDdJx99e8L2IW0JjHK1Bx96d8dX4MjFCM2oDGPGaAizwl9QmckmqmKPXxK//R2HeAdWCftPhzBpTMrC8vmpbytsjqMsi/ZjgC9ty9OmdKnis8B2bzpnniXanVZeHuc+4+4O6DwAopk1V3fwM+zGwszy+XiZcFNJ4f16QGXv2jp0ngviC1AY15vAATZtZpZl2khdOHAtXH77h7ywYp7MP8uAO4JBXqEvCYx2IrP0O7xw8ZlElrDZWaMZz3GQKucjYHQHe7j6HV9VDz+gJpDrX6fBS4I60/bJNvqIsympwf08ANcAvskhbbQ9dGkzymSM3+gbQes1WU+vjL0J2nIiLB6M5TEZFg1NhFRIJRYxcRCUaNXUQkGDV2EZFg1NhFRIJRYxcRCUaNXUQkmC/vI58q6K3C5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb4453358d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AR_model.get_sample(3)[names].transpose().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear autoregressive models\n",
    "The flexibility of Brancher allows you to easily specify more complex models. For example, let's now try to construct a more sophisticated autoregressive model with nonlinearities and variable standard deviation:\n",
    "\n",
    "$$ \n",
    "\\boldsymbol{\\mu}_t = b ~ \\tanh{\\left( x_{t-1}^3 \\right)}~, \\\\\n",
    "\\boldsymbol{\\sigma}_t = 1 + c~x_{t-1}^2~,\n",
    "$$\n",
    "\n",
    "In order to implement this model, we need to import the tanh function from the brancher.functions module. This moduls contains every single function present in pytorch, including all the neural network functions that you will probably need for more complex models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb4452a90b8>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb445319b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from brancher.functions import tanh\n",
    "\n",
    "# Model parameters #\n",
    "T = 100 # Time horizon\n",
    "b = 0.04 # mean autoregressive parameter\n",
    "c = 0.1 # SD autoregressive parameter\n",
    "\n",
    "# Initial distribution\n",
    "x0 = NormalVariable(0., 1., 'x0')\n",
    "x = [x0]\n",
    "\n",
    "# Time series\n",
    "names = [\"x0\"]\n",
    "for t in range(1,T):\n",
    "    names.append(\"x{}\".format(t))\n",
    "    x.append(NormalVariable(b*tanh(x[t-1]**3), 1 + c*x[t-1]**2, name=names[t]))\n",
    "AR_model = ProbabilisticModel(x)\n",
    "\n",
    "AR_model.get_sample(3)[names].transpose().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coupled autoregressive models\n",
    "We can now couple the value of multiple variables. For example, let's $y_t$ gives the standard deviation of the process $x_t$:\n",
    "\n",
    "$$ \n",
    "\\boldsymbol{\\mu}^{(y)}_t = b^{(y)} ~ y_{t-1}, \\\\\n",
    "\\boldsymbol{\\mu}^{(x)}_t = b^{(x)} ~ x_{t-1}, \\\\\n",
    "\\boldsymbol{\\sigma}^{(x)}_t = 0.1 + c~y_t^2~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'y time series')"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb445128dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb445041588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Model parameters #\n",
    "T = 100 # Time horizon\n",
    "b_x = 0.8 # x autoregressive parameter\n",
    "b_y = 0.99 # y autoregressive parameter\n",
    "c = 0.2\n",
    "sigma_y = 1. # Standard deviation of the Gaussian input\n",
    "\n",
    "# Initial distribution\n",
    "x0 = NormalVariable(0., 1., 'x0')\n",
    "x = [x0]\n",
    "y0 = NormalVariable(0., 1., 'y0')\n",
    "y = [y0]\n",
    "\n",
    "# Time series\n",
    "x_names = [\"x0\"]\n",
    "y_names = [\"y0\"]\n",
    "for t in range(1,T):\n",
    "    x_names.append(\"x{}\".format(t))\n",
    "    y_names.append(\"y{}\".format(t))\n",
    "    x.append(NormalVariable(b_x*x[t-1], 0.1 + c*y[t-1]**2, name=x_names[t]))\n",
    "    y.append(NormalVariable(b_y*y[t-1], sigma_y, name=y_names[t]))\n",
    "    \n",
    "AR_model = ProbabilisticModel(x + y)\n",
    "\n",
    "sample = AR_model.get_sample(1)\n",
    "sample[x_names].transpose().plot()\n",
    "plt.title(\"x time series\")\n",
    "sample[y_names].transpose().plot()\n",
    "plt.title(\"y time series\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inference for time series models\n",
    "\n",
    "Now that we know how to specify a model, we can use Brancher to perform (variational) Bayesian inference on the latent parameters. For example, let's learn the autoregressive coefficient ($b$) and the noise parameter ($\\sigma$) of an autoregressive model. The first step is to specify prior distributions for $b$ and $\\sigma$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "from brancher.standard_variables import LogNormalVariable, BetaVariable\n",
    "\n",
    "# Prior #\n",
    "sigma = LogNormalVariable(0.8, 0.2, 'nu')\n",
    "b = BetaVariable(1., 1., 'b')"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Let's use the AR(1) for analyzing some real world finance data. We can get a realfinance time series using the pandas datareader:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "232"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rDhCPtVUFKAUHzw6ka6qCkDQTK+HGWvoSyE2OjBX9rmHD3VCW5+LOi+sY9Btui4r89Pn0wRBFi6umEc+Fxm5TPPbJq3n5L6/DpmD78W6eONjOprpCKvKnvlHm5jhYVpbLwZj0z76RIJ/+2R72NvenY+qCMCOW6F9QWwjA0pLcqE9fArnJkbmib/atLc/L4epV5dEA7kJY+mC4eSrSGE+YDQVuJ1WFbjbXF/F/b7Swr2WAWy+onnG7DTWF0Zz/fl+Qd//3a/zfG618/pGDEuAVMgJL9P/orSt4+4ZKVlXm4bQr7DYlln6SZKzoW//ksnwjRfNdFxmrSVO9MGsi5fk5rK3K5x1ZlNJ49apyWvqMngO3JCD6G2sKaO0fpW8kyH+/eIqjHUPceXEde5v7pZ2jkBF0m0bgFSvL+PZ7tuJ22lFK4XXaxaefJBkv+uVmiuIfvmU5f3PbhuiCjHTy+Cev4WPXrkj7cWfLNWbsYXNdIfUlM/cK3lBjPDIfahtkX+sAayrz+ft3XUBtkYd/ffp43NLPh84O8gf//VpSTeUFYbZ0Dwdw2W3kT+iM53bZxb2TJBkr+l1DARw2RaHZWLzI6+J9VzQsWPZMpmTtJMLm+iLWVRfwB5cl1hLxXAbPAIfbBllfU4DLYeOTN6xib3M/D7/ZOmmbX+5t5aUT3XzlsSPzOndBiEf3cJCyPNekz6HHaWdUau8kRcaKfvdwgNI8lzTwngVOu43H/uRq7tpan9D44lwXNYVunj/aRddQgHXVxk3gji11XLSkiH947AiD/rFx2+xo7EUp+PnuFnaf6Zv3v0EQYukeDlAWJ4nDK5Z+0mSs6HcNBShPc6bOYmZ9TSGvnDRaKK43Rd9mU/ztbRvpHQnwuYcPRIO6w4EQB1oHeN/lDRS4Hfx81+SGMwvFwbMD7G+R9NPzje7hQHQ1eixu8eknTcaK/pleX7TevJB6NtaeS021RB+MzmKffttqHtl7lp+a3cR2ne4lHNFcv66CZeV5tJqN6p8/2rmgPv5/euIo7/iPl7jnezsJhaWxxvlE93CA0lzXpNe9LrusyE2SjBT9UDhCc6+PhrKZa9II84MVzK0t8lA4odTER69dyeb6Ir7/ymkAXjvVi8OmuHhpMTWFbs72jzIcCPH+77/OA+aYdNPYNcw3njvB6sp8ekaC7Dw9qxYOQgYSiRir8+O5dzxi6SdNRop+24CfsbCmoVQs/XRhBXPXxVj5Fnab4uIlxTT1+tBa8/qpXjbVFeJ1Oagu9NA24OdMzwhaw5ke36Tt08HZfmMx32duXovHaefR/dIV7HxhYHSMUETHde94xKefNBkp+qe6jZ64DQlUnxTmh+pCN1uXFnPDuoq479eXePAFw/SMBDnWMRR9MqgpcuMLhjnQavjRm3qnFv2RQIjvv3yKcJwU0LnSNmC4mJaX5XHd2goeP9CRkuMI6adnxFyzkzfZvWNk74joJ0NGiv5psxG6uHfSh1KKhz56BXdvWxL3fSu+sre5n0F/iGXm/8Yq0vaqGQRu6Zta9B/a3cIXf3WI1071zOfUAaJVQisKcrj5giq6hwO82SRZRecDp7uNa6o8jqUv2TvJk5Gif6p7BK/LnvY6O8LUWIu8tpsrdJeVG6JvNYrf0Wj40LuHg1P2LH3RLACXaJvHZGgb8FOa68LttHPREqP5zbGO4Xk/jpAeWvtHufO/XuF7L5/ib399iJpCN5vqiyaNc7vEp58sGdk560yPj6WluVm1IOp8x2rivv14NwDLTUu/1rT02wfP1eNv6Rtl9YSmLWPhSPRp4GAKRL99YJTqIuMGVF3gJsdh41S3iH628ne/PsSuM33sOtOH3ab46b2XRbvXxeJ1OgiGIoQjOm0d9bKdjBT9090j0UJnQmaQm+OgNNfFqe4RnHYVFfuyvBycdsVYWFNX7KGlb5TmXt8k0X+zqZ+RYBivy56SMs5tA37qTBeUzaZYVpYbjQ0tFH/84zepKXLzmZvWigGTBC+f6OaxA+18+m2rqSny4HHa2doQv4+Gx2U4K0bHwnFvCsJkMs69ozGCgeLPzzzqTBfPkhIvDrtx6dhsKtrNzCo93RwnmPvS8S5sCu66uI4TncPzHnxrG/BHXU0Ay8pyaVxg0X/2cAfffqGRL//m8ILOI9v46evNlOXlcO81y7nz4rpJfZ9j8ZiNVCSYmzgZJ/pjoQihiGZpAoXChPRSb7p4lpWNL3pXU2i8ftGSIjxOO029o+Pef2TvWR549QxblhRz+YoyItpofzlf+IIhBkbHou4dY465NPX4GFugRVr+sTAjwTD5bgf//dIpuoakMF2itPaPsqoiD7fZJGU6pJFK8mSc6FtpdiVxVt8JC4sVzF1ePv4prMYU26WludQVe2iOyeD592eO84kfv8mysly+dtfmce0Z54t2M3NnoqUfiuhoiel00+8zahVZPZ7P9CzsU0c20dY/Ou4GPh1eaaSSNBkn+hGzvovV/1LIHKy0zWUTXG/Vpn9/SYmX+hJv1L1z/0un+JenjvHbW2p56A8vZ1mZcVMo9DhTIvpVBed6/Fo3poUK5vb5jPrvF5oZJ6cXaNFathGOaDqGAtGnx5mwLP2pMsaEyWScslrraawAjZA5rK02grOWtW5x6wXVjAbDVBW4WVGey4vHu3j6UAdfefwIN6yr5Gt3bo5mViilWF9dwKF5DOaejWPpLzddUI1dI1y3dt4OlTB9I4bob6orxKbE0k+UziE/4YhO2NKf2DIxGIrgcoh2TEfGnR3L0vc4M+5+tOjZsqSYl/7yrWyqG58vvbG2kC/etgGbTXHvNSso9Lj40A92YVOKL92+YVIq3YaaAo60D81bUbR2czVubCvN4lwXRV7ngmXw9JqWfmWBm9pij1j6CWKV00jW0h8Nhukc8rP5b56Ubm8zkHGir6PunZmDOEL6qZuh8ml5fg5fv/tCHDbFp962iuo4H94NtQUEQhFOds2PIB/rGKY8P2dS4G91RT47Gnvidv5KNZalX+x10VCaS5NY+glhldOYjU9/b/MAo2Nh3pD+DtOScaJvfT5F9LOXK1eWsftzb+Pea+K3mNxo1u2ZKV//P58/wb8+dWzaMf6xMM8e6eS6NZNrBr3n8qWc7Brh0QPpL77WO2IEcou8TpaWesXSn4KJN+S2fstVl5il746x9A+3GXGi03KDnZYMFH3jInCL6Gc1E8szx7K8PA+30zZtMDcQCvNfz53kB6+ejj79xeOl490MB0LcfEHVpPduuaCalRV5fP3p42kvvtbnC5LvduC022gozWVgdIx+0+UjGDx+oJ1Lvvz0uHpNZwdGyXXZKXAn5t6NtfSjor/A6zMynQwUfeO7N4EcXSE7sdsUa6sKopU54/HS8W6GAiH6fGPTVu58dH8bhR4nV5oLwyYe51M3rOZ45zCf+d99aXXz9PmC0bTjpWa1WMvaX6i1A5nGobMD9IwExy1ea+v3U13kSXgFs5Xl1zsSjIp+Y/fItIbCYictoq+UukkpdVQpdUIp9ZnpxkYiGpfdFl3xKZyfbKgp4FDb4JQfzkf3t0cDwHua++OOGfSP8dShDm5cX4lziuvl1k3V/Mn1q/j57ha++dyJ+Zl8AvSOBCn2GqJv9YU40zNCY9cwW/72KR4/0J62uWQqXWaXtccOtPPyCaOmU9vA6LgsrJnwuOxsri/ikT1nOdProzTXxZA/RO/IuaeqtoFR/vGxIwRDcrOFNIi+UsoOfBO4GVgP/J5Sav1U4yNa43aK4J/vbKorZMgf4mTX5Dz6YCjCU4faecematxO25Si/29PHWc4GOJ9VzRMe6xP3rCKbQ0lPHmoYz6mnhCxln59iRe7TfGrvW188VeHGAqEeEPKPtM5GGBFeS5leTn8eGcTYKTfJpq5Y3HnllrTuocbNxhuvli//ud/eZBvvXAyJSW9s5F0qOs24ITWulFrHQR+ArxzqsERLQuzFgNXrDDcMS+aVTtj2dHYw6A/xDs213BBbSF744j+0fYhHnj1NL+3bQkbawunPZZSim3LSjjUNpi2RTx9I2NRS9/ttPOZm9by9OEOth/rQimjveNip2s4QF2xl+vWlvPCsS58wRDdw4GEM3cs3rG5Bpf5pHeLGdt5s6mfL/zyAP/y5FGeMm/2b5yJbzwsNtKhrrVAc8zvLcClUw2OaC2ZO4uA+hIvy8pyefF4N++/ctm495490onbaePKlWXsaOzhgVfPTFp0809PHiXXZefPb1yT0PEuXlpMOKLZ09wfveGkkt6RICW554LZH75mOUrB66d7iWg40Smi3zUUYE1lPtetreRnu1r40q8Po/W57K5EKfK6eNv6Sl452c2ly0qx2xT//OSx6IKtpaXGk9ZueboCMiSQq5S6Vym1Sym1yx8IJFRoSch+rjJFPdbXqrXmmSMdXLWyDLfT8NcGQxFej2l0fqB1gKcOdfChq5dTnGCNpi1mY5V05HD7x8KMjoUp8o6f24euXs6337OVtVX5NPX6CIQWb72YSETTNRSgPD+Hq1aV4bQrfryzybwJxG/ZOR1/d/tGfvaRy3E5bCwp8TI6FuaeKxr4xR9dyf98+DIuXVbKm019C7JmI9NIh+i3AvUxv9eZr0XRWt+ntd6qtd7qdLrE0l8kXLWqDF8wPK6t4YnOYZp7R7lubSUA162toLrQzZd/c5hwRBMIhfnqE0cpcDu458qGhI9V6HWyqiKPXWkQfavuzlRFA1eU5xGOaJoWce5+v9nsvDw/h7wcB5cuMwrT/fH1K7HNohlKca6LVWYPh1UVeZTkuvjU21ZzYX0RtUUetiwpmjKGtNhIh3vndWCVUmoZhtjfDfz+VIPDER2tpyGc31y+ohSbgpdP9nCpWY3y6cOdAFFrz+ty8Nlb1/Hx/3mTj/xwF829oxztGOKvf2s9Be6p1wLEY2tDMb/Z10YkomclLInSG7MaNx4ryo26QCe7RhgOhHhk71nWVRXwO5fUxx1/PtI5ZPY0zjf89x+4qoGyPBc3b5y6dn6i/N3tG/GPRSj0nLs+Ll5qPOntPtMXvTksVlIu+lrrkFLq48ATgB24X2t9cOrx5+ppCOc3BW4nDaW5HO8Yir72xMF2NtYWjKujc+sF1Wzf2sXzR7so9Dj57vu2cv26yqSPt7G2kB/vbKZ90B9t6J4K+szVuFNZ+lZ/4e+9fIrXThluqxyHjWvXlkdF8HzH6i9QbvbBvm5tZfTpbq5UFEw+h8vKcinyOtnT3M/d25bMy3GylbSkyWitHwUeTWSsBHIXF8vL86KP3K39o+xp7ucvbhofnFVK8dU7N8/5WJbQtw2Mpkz0Owb9fOO54wBT5pvn5TioKnDz2qleVpTn8vW7L+K2b7zEd7Y38tlbp8xmPq+YKPqpRinF6op8ce+QIYHcWCJaR1ugCec/KypyOd3tIxSO8Nh+o0bOLfPwiB8PK//bquSYCv78oX3sbR7gq3dsijadiceKCsPa/+JtG9hYW8jtF9byox1N0UJt5zudaRZ9MM75fBX5y2YyUPSl2NpiYkV5HsFwhJa+UR7d38b66oKU9Ue2Onyd7U9dN63WPh/Xra2Y0T//+9uW8onrV3H1qnIA7ry4jtGxMIfapq5H9PiBdr7y+JF5ne9C0TUUwOuyp7WZ+fKyPHpHgrOugdQ3EjwvMq4yUPS1+PQXEVZQ88UT3bzR1D9tE+y5ku92kp/joG0gdZa+LxhOyGi5dVM1n37b6ujv1lNB64Qb0uMH2vjcL/YTiWi+/sxx/uv5k9EaM9mMla6ZTqxuarOx9rXW3PT17bz9X7fPuJp60D/GSCBzO3llnOgDkr2ziFhhfhC//cJJAG7eOLla5nxSXeSeJKzzyXAgRO4srNfKAjdKQWtMT99f7zvLxx58gx/taOIHr56Oiv0PXj0zX9NdMDqH/JTnpVf0z2VNJe/Xb+0fpWMwQGv/KO/97s5p6/h85Ae7+ezD+2c9z1STkaIv7p3FQ5HXRVmei5a+UdZW5bPc/GCmipoiT7RRx3yjtcYXDJObk/z163LYqMjPibqeRgIh/vzn+9iypJjy/Bz+/lHDrXPN6nJ+8WYrA6Nj8zr3dNM1FKCiIL2iX1fswWlXNM7C0j9mZpj9ztZ6hgMhmnqn3sfxzqHYn4FwAAAgAElEQVSMjh1kpOiLe2dxYQn9rRekzrVjUV3oiTbqmG8CoQjhiJ6VpQ9QW+ThrHlDeu5oJ6NjYf787Wv4/W1LCIYjbK4v4lM3rGJ0LMz2LG4JqLXmbL9/XCP7dOCw21hamjsrS/9ou7HNTeaT6InOEXzBEK+f7o1+dQ8HGAtH6B4O0jGYOhfiXMnINBlx7ywuVlbksfNUL7ek0J9vUVPopmckiH8sPGO5j3949DB1xR7ec3lDQvu2/Li5s8w+qynyRBvLPLa/nbK8HLY2lNBQlst3XmzkXRfWsMT0/fdmcZZPz0iQ0bEw9SXpFX0w3IknOodp7BqmtthDjiMxrTnWMUR1oZsL643+0I3dw7x4vIsHX2uKjtmypIj/+P0tAHQPBwiFIxlZIj7zZoRU2VxsvPvSJfzlTWujPtdUci5Xf3pLbDQY5nsvn+Ybz51IuF7LSMDI7JiLpd/aP4ovGOLZI53ctLESu01RWeDm1c9cz3svb4iuMu33Za97p9lsijNTv+VUYKwLGeG6f36B72xvTHi7o+1DrK7MJ9/tpCI/h8auEXY09rCtoYQfffBS3r6hkuMdw7Sb11VEGze3TCQjRV/cO4uLDTWFfPTa+P1055vqBNM232zqIxiO0DEYSLj2/XDU0p/d9VtT5CEYivB/b7QyOhYeV5Kg0OvEZlM47Dbycxz0j2amoCRCixmsXghL/7c2VXPrBdWU5bmmbdcZSygc4UTXMGuqjPINy8tzeaOpj5NdI7xlTTlXrSrjkoYShgKhqO8fjH4BmUhmir64d4QUYS3Q+ofHDvO++3dOacXvONWLTYHLbuPR/Yl1ubJq9c/W0reeQu5/6RTFXieXLiuJO67Q62QgTZZ+x6B/xgb2ydJs9sStXwBLf0NNId989xYurC9K2Ld/ptdHMBRhdaUl+nnRYLBVvdVKuY2tBpupfv2MFH3J3hFSRVWhkRp5oHWQF451TWnt7WjsYWNtIdesLuexA21xbw4Do2Pc8C8v8L+7W4AYS38W2TtwbvFYY/cIb99QNaU/uMjrpD9N2Tv//ORR3nf/znntOdvcO0pJrmvWN8f5YHl5Hqd7fIQTcN0dazes9zWW6JuLB+02xeZ6o/b/kniiPySinzAi+kKqcDvtfP3ui/ju+7aiFDxzZHILRf9YmD3N/Vy6rIQb1lXQNuDnTJzm7Mc7hjjROcyfPbSXX+5pxRecu0/f4uZpMpmKPK5ZrypNltb+UbqHg9F+tvNBS5+P+uL0u3ZiWVGeSzAUGbcuYioauw2r3lrctaLCiD2tq86Pxh8tS7+5d5Qqc81Fh7h3Ekd8+kIquW1zDdevq+Si+iKeMUs5x/L66V6CoQiXLiuNppM29/r41d6z3Pz1FwmFjYU5Z82gXVleDv/53MkYn/7sRL/Q4yTXZafQ4+SKFaVTj0ujpW8J19H2oRlGJk5zr29BgrixWP/Xk90zu3iaenyU5eVEb+YryoxtLdcOGEX0Ss2qqrXFHsrycugU907iiE9fSAfXr6tkf+vAJN/rgzuaKPI6uXJlWTTY2Nzn46Xj3RxuG6TZtA7bzGDwZctL6RkJ4AvMzaevlOLihhLuvLgO5zSpfkWe9Pr0Yf5EPxLRtPaPUrcAQdxYLBfNyQTaVp7pHWFJzHzrij184Mpl3H3J+BLNlrVfVeCmsiAnWlQu08hM0RdLX0gD168zGrU8efBcoLa1f5QnD7Xzu5fU43HZqcx347LbaOr10WhahVaGRtuAn/wcB0tLvPT5xhjyG6I/F/fkDz6wjc/dum7aMZZPfz797PHwBUPRv2m+RL9jyM9YWC9IEDeWklwXhR5n1HUzHU09PpaWnisCaLMpPv+O9ayvKRg3zvLrVxTkUJHvnnUg9z+eOc5v9rXNattEyDjRV5CRCxqE8481lfmsry7gRzuaogL64A6jrs17LlsKGB/w2mIPLb2jnDIFwmpq3to/SnWRm5JcF+GIpm3Qj8OmyHHM7fpVavquXkUe43jDKS7qFeuTjk1FnAvNvVa65sKKvlKKFeW5NM6QwRMIhWkb9EcFfTqWTLD0Z+vTf+DVM/xq79m47z2y9yxf+vWhWe3XIuPU1TbDBS8I84VSinuuaOBoxxA7Go2si+eOdnH5itJxPue6Yg+H2gbpHjaCp8ejlv4o1YUeSvMMX25zrw+vyz6jaM+VQm96FmhZluqaynyOdQzPS1Nxa31EbdHCdwhbXp7Hic7haTN4WvpG0RqWliYh+oVuKvLd9IwEovGfRNFa0+cLMhSY/L/VWvPPTx7luy+dmlOl1cwT/RT2LhWEidx2YQ1FXicPvHKaYCjCic4hNtUVjRuzpMQbtfKddsWxDsM6bOs32i5avXBb+kbTUh++yFyVm+qia5boX72qjNGxcDS/fi5Ee+PGaWmYbq5fW0H3cJCfvN405RireX0ilv76mgKUMsqKVBa40Zqks54G/SHCER11q8XyRlM/Z8z5zKXSasaJ/kKncgmLC7fTzjs31/D8sU4OtQ0yFtasqx7vq411RVy5soyTXcP4giF6RoLUFLqjvXBb+0bxpkP0zZtMqi19a0XpNauNRi/z4dfvGAzgcdrJX8AcfYubNlZx6bIS/umJo1MGxs/0GDf7JQlY+htrC3n9szewoaYw4ZXfE7E6pw3GuaH/3xstuJ02br2gml+82cqj+9tmFTfIONFfyAUbwuLkipVl+Mci/GSnYfGtnyj6pqvHpoyMn0Aowk6zoXl1kScq+sFwJC3Xb5Hl3klxKYaOQT8ep52NtcYCpOYEctpnotMsqZxqF1giKKX4wjs20D86xv0vn4o7pql3FK/LnnDt/zJznGW8tiR5znrN9RcTLf2xcIRf72vj7Ruq+NhbV+APhfnYg2/wjv94KenYTsaJviCkm20NRrmDh99sxe20sWxCu0YrbbOu2MsGM2Nj+7FuwFhFa4k+zL7uTjKkzb0zFKCyIIdirxOvy57QQqaZ6Bz0U5HmjlnTsb6mgLesLufHO5sYi+N/b+odYUmJN+mbVG2RtVgrOZeYZelPFP2uoQADo2NcuqyUDTWFbP/zt/KtP7iYzqEA33j2RFLHENEXFj3FuS7WVuUTCEVYU1WAfUJcybL0l5XlsqoiD7tN8cjeVsCo5eN22qNpmumw9AvSVGmzY9BPRYEbpRS1RR5a5sGn3zUUoCJ/4f35sbz38qV0DgV48uDk1dlnenyzyjTyuOyU5eUkb+mboh8MR/CPhSe9XmYmDdSXeLlpYxV3bKnj/pdOJfW/EdEXBIwFVjDZtQOGO6WyIIcNNQXku5184rpV0UyeqkJDwCxrPx2Wvttpx+O0p9zS7xz0U2kGXOuKPfPSZrJzAXrjzsRbVldQX+LhwdfGB0cjEU1Tr4+ls0wvrSv2JB38ju2TEGvtd5sB4dIJbqZPvW0VwXCEX+1NPK9fRF8QgMuWGy6e9dX5k95TSvHrP76aT1y/CoCPX7eSK1eWUl/iiTZisZbgpysmVehxprT+jtaajsEAlaZA1xZ7krZaJ+ILhhgOhNLeJnEm7DbFDesqebOpf1xaatdwgEAoklC6ZjzqS7y09I3yWmMPH/7BroTSN3tj/qeD/nM39Z7h8Za+RV2xl811hTx+QERfEJLiLasreM9lS7lpY/xCZ+X5OVGBt9sU999zCQ9/7Mro+8Wm6KcjZRPMVbkpdO8MB0KMjoWjAl1b5GVgdGxOC8KsbKBMc++AkbM/OhamPSYbxkqPnO1CsrpiD2f7R3nwtSaeOtSR0Orfviks/Z6R+JY+wE0bq9nbknj5axF9QcDwwX7p9o0Jux5yHPZopgacc++kq+tboSe1RdcGTcGxOnXVmdkocwnmWrVoKjPM0gej6iYwrmm6la4ZW4IhGeqLvYyFNU8eMsp8JLKgqnfk3P90aIKln+OwxXUf3mz27U0UEX1BmAdKvJZ7Jz11o/JyHNGevKnAEpx8tyH6tdEUxNkHc6MLszLQ0rdadTbGVN1s6vVhU+NLXieDdaP0jxluncNtM69z6PMFoy6c8T79IGV58VNdG8pyWVs12S05FSkTfaXUXUqpg0qpiFJqa6qOIwiZQEleen36NptKqAHIbLEEx3JX1ZnCN5dgbkfUvZN5ln5Ffg65Lvs4S7+p10dNkQfXLGspxbqFyvJyErL0+0aC0SeL2AVaPSOBaLmPeHzz3VsSnlcqLf0DwG8D21N4DEHICM5Z+ukRfUeKRX/YFP18t/H3lOXl4HLY5hTM7Rzy47LboovLMgmllNk0/Zylf6bHl1D5hamoKTKaqTSUerlmdVli7h1fMJotNM6nPxyMJgvEw3pSSYSUib7W+rDW+miq9i8ImUQ6UzbBCCaHU1haeTDq3jFE32YzcvXn4tPvGjTSNTNhNW48jKqb4y392WbugBH3WVtVwE0bq1lfXUDnUICeaWrxhMIR+n1j1JV4UWqiTz8QN4g7G6TmgSDMA+uqCyjLy0nK4poL9lRb+gHL0j9nlc8m7zyWjiF/xuXox7K8PI9f7DnLaDBMKBKhdyTIkpLZBXEtHvn4ldiUYkdjDwBH2oe4cmX8c2AF5svyXOTlOKLBdK013SPBad07yTAnS18p9bRS6kCcr3cmuZ97lVK7lFK7urq65jIlQVgQ6ku87PrcDTSUzU0kEsVuU4TC6fPpg7EiubFrZFbNW3qGA7x+uo9NdYXzNsf5xuqBe6p7hKbexKtrTofTbsNuU9FA66GzU7t4rHTNYq+LArcz+rQ1HAgRDEUoy80AS19rfcN8TEJrfR9wH8DWrVtT2w5IEM4DHDZFJIXunWF/CJsa3wVsRXkew4GQUUohydLIP93VTDAUiTanyUSsp7QTXcPYTRfUXNw7sZTm5VBf4mH3mT4+PMUYazVuSa6LfLcjeuO1FmbNl6Uv7h1ByELsNkUopdk7Y+TlOMb532NFMRnRD0c0D+5o4ooVpayqTDy1MN0sL8/FblMc7xhCKYXNrI0/X2xrKOW5o51orePGNXpiRL/A7Yz69KdbmDUbUpmy+S6lVAtwOfAbpdQTqTqWICw2Uu3THwqExvnzAVZUmM3Eu2ZeWRrL/tYBWvtH+d1L6udtfqkgx2FnWVkuR9uHONY+RENpbnQV9nxw6bISekeC4zKEYrFq71cXusdZ+ladp+myd5IhZZa+1vph4OFU7V8QFjMOmy3lefpW5o5FVYEbr8s+Y1/ZiViF4eqyoEHSmsp8Dp4dwKYUq+f5qWTbMqO+02unellZMXnfbQNG/4JCj5N8t4NjnaalH627k+GWviAIqSPl2TtxRN/IZc9N2tL3mZlA6SpRMRdWV+ZzptfH6Z4RViexyjURlpZ6qSzIiTbgmUjbwCjVRUYp6wKPM2rpWzfZknmy9EX0BSELMXz6yTXdToahwFjc4nEryvM42ZmcpT8SNOrC52aB6K+pykNriGjD6p9PlFJsW1bKr/aeZcuXnuKFY+MzFc/2+6kpNJ6GLPfOnuZ+vv/KaW65oGrWK4MnIqIvCFmI3aZIoeablv7klbMryvM4OzDKaDAcZ6v4+IKGxZquukRzIdals6Zq/tdc/NFbV/C+Kxpw2BT/9fz4jlftA/5of4Z8t5NwRPP+7+2kssDNP7xr07zNQURfELIQR6otfX+IPPdky3x5eS5aw4kkrP2RgGnpZ0H/66WlubgcNlx226yra07H2qoCvvCODbz/ymXsaOzleIdRhC0UjtA55KfGFP01lfm4HDYuWlLMd967lcJ5LF0hoi8IWYhNKSKahBZKdQ76+Z1vvcpLx7sT3r+RvTNZpLc1lGBT8MTB9oT35QsaOf858+SeSCV2m2JVRR7Ly3Nx2lM339/ZWofLbuOHO4xuXR1DASIaqs3Cdm9dW8HRL93E/fdcwvqayd3c5kLm/xcEQZiEw+zjO1MwV2vNZ39xgJ2ne/l/D+8b13d1KgKhMMFQhII47p2KAjdXrSrn4Tdbx3WZmo7hQIhclyNja+5M5Iu3beBvbtuQ0mOU5uXwtvWV0b68bTHpmhapOl8i+oKQhdjthiDMtEDr8QPtPHWog1suqKK5d5T7tjfOuO/hOCUYYrljSy2t/aPsONWT0Fx9gTDeLPDnW1zSUMKlZs/kVLKhtoD2QT9D/jHaBoxeA9WFqU9rFdEXhCzEKhMwk6X/xMF2KvJz+Pe7L+Itq8t5aHfLjPsemlBWeSI3rq8iL8fBI3vOJjTXkWAoKzJ30s1Kc4Xzya4R2gZMS78o9Q1mRPQFIQuxW+6dGXz6J7qGWVtdgMNuY111AW0DozO6ZawKm1NZ+h6XnTVV+dEesjPhC2aXpZ8urJIUxzuGONvvJy/HEdelNt+I6AtCFhL16U9TaTMS0ZzsHIn2f60pcjMW1nSPTF3THWJr6U8tQCW5rmiBsJkYCYilH4/6Yg8uu40TXcPGwqzC9LSRFNEXhCzEsvSn8+m3DfoZHQtHi4ZZ/uK2fv+0+57YNSsepbmuaIGw93z3NX746ukpx/qC4axI10w3DruNZWW5HO8YZl/LAMvSVJZbRF8QshC7zfjoRrTm0z/bw1cePzJpjJVLb/mOLUvS8h9PxUw+fTAs/T5fkLFwhJdPdPNGU/+UY0eCoXElmoVzrKzMY/uxLtoG/PzW5pq0HFNEXxCyEEeMpX+wdZD9LQOTxkRF37T0a8wc8LMxln48//5MPn0wRD8c0ZzuHiGiod83tatH3DtTs7I8j1BEk5/j4Mb1lWk5poi+IGQhthiffigSiZY6iOVE5zBFXme0UFex10mOwxa19H+97yyb/+bJSZa/Vcc93opcC6uhx+F2Y0Wp1eovHtmWsplOVlUaN+SbL6ia1zLO0yGiLwhZyDlLP0IoovHFqYVzsnOYleV50UU+SilqijycHfBzunuEv3xoH0OB0KSSCvtbByjPzyHHMbUIlZit+w63Ge3/+n3xRV9rLSmb03Dx0mJqizy857KGtB1TRF8QshArkBvRmlB4CtHvGp7U+am60E1b/yh//csD0SBwx6CRzRMIhekbCfLskU5um8G/bDX0OBIV/fHuHa0139neSNuAn4jOjro7C0F1oYeXP3MdF6Sxd7D8JwQhC4nN3glFIgQmeHcGRsfoGQlGm31bVBW6eepQByOBEB++ejnf3t5Ix6Cf3+xr409/voe3ra9iLKy5Y0vdtMe3XEZHTPfOwOgYkYiOup0au0f48qOHGQpkT4XNxYJY+oKQhURFP2xY+qMTfPrNvcbCqSUl40W/ptDDkD9ERMO7ttRS6HHSOehnf+sA/rEIv9p7lrVV+TMW+bJE3yofENHnsn4A+sx0Tqv2fjY0UFksyH9CELIQR4x7ZywcwTcWHtdw21otu6TEO247a5n/8rJc1lTmU1mQQ8dgALs9SFWBmw01Bdy1dXorH8DttJPrskcbpAD0jwajJYD7TB+/FS/IlZTNjEFEXxCyEFuMeycc0WgN/rEIHlNcmyxLv3S86FudmW7aWIVSisoCNx1DfiIRzcqKPL57zyUJz6Ekz8VI7yg2ZVj6fb4xlpp1yvpMH/+pbqO1old8+hmDuHcEIQuJLa08ZgZkY9M2m3p9lOa6JuXaX1hfxFUry7j7kiUAVOS76RwM0Nw3Sn1JchUerQyeBrPZSGww13LvBMNGoxex9DMHuf0KQhZijxH9kCmsvmAYqyBwc6+P+gmuHYDiXBc/+tCl0d8rC3JoH/QTjmjqiiePnw4rg2d1ZT6N3SPj0jb7JqRwSvZO5iCWviBkIQ6zDMNYOIK1qDY2bfNM78gkf348Kgvc0fLM8W4S01ESFX0jLTTW0p+Ywil5+pmDiL4gZCFWJ79g6FyfXMu9MxaOcLbfz9LSREQ/J/pzfXFy7h3L0l9plgiOXZU7sQKnrMjNHET0BSELsQqu+cfOif6oaem39RvumkQs94qCc+V8k3XvWJZ+daGbfLdjnHun3zdGoedcaWax9DMHEX1ByEKsQG4gdM6lY7l3opk7Cbp3ADxOO2VmPZ1EWVrqxW5T1Bd7Kfa6xgdyfUHWVxu5/kqB2ylSkynIf0IQshCbskT/nKU/Yrp3TvcYaZKJuHfK8wz3Tl2xJ+lG3Deur+L5P7uWqkI3RV7nuOBtny9IQ1kuHqc9q5qiLwZSJvpKqa8ppY4opfYppR5WShWl6liCsNhwmI3R/WPnLH3LvfPckU6qCtxU5s/cicnlsFGa60o6iAvGWgFru0KPM+rT11rT7xuj2OukusgttfQzjFRa+k8BG7XWm4BjwP9L4bEEYVFht0229H3BMN3DAZ4/1sXtF9VGF3DNxCeuX8V7Ll86p/kUe10MmO6doUCIUERTkuuiptAj6ZoZRsr+G1rrJ2N+3QHcmapjCcJiw265d2IDuWNhfrnnLOGI5re31Ca8r/dd0TDn+cS6d6yFWUVeFx+4qoHuocR66QrpIV234A8AP03TsQThvMey9P0xgdyRQIjHD7RzQW0hq800ynRR5HUx6B8jHNFR8S/2OrlubXq6QQmJMyf3jlLqaaXUgThf74wZ81kgBDw4zX7uVUrtUkrt6urqmsuUBGFREM+n7wuGOdo+xBUrSqfaLGWU5rrQ2gjgWnV3inOTywYS0sOcLH2t9Q3Tva+Uugf4LeB6rfXkZpzn9nMfcB/A1q1bpxwnCIKBPU72Tmv/KMFwJJqGmU7KzCygrqFA1L1T7BXRz0RS5t5RSt0E/AXwFq21L1XHEYTFSDSQG+PTtypaVhWmX/TL8w3R7x4OjHPvCJlHKrN3vgHkA08ppfYopb6VwmMJwqLCqr0T69M/Y+bnL4Slb4l+11CAfl8Qm4ICt4h+JpLK7J2Vqdq3ICx2TM0fZ+mPhQ3P6EJY+tZq3u7hAN3DAUpyXQmnjArpRVbkCkIWYln6VhkGq8yBUlCRnzPldqkiL8eB22mjayhAc+8otUnW8RHSh4i+IGQhE336VnGz0twcnPb0f6yVUpTl5dA9HKSlz5d0xU4hfYjoC0IWYp9QcC3f9J9XFabfyrcoz8+hfcBPa/9o0hU7hfQhoi8IWYjlLrdSNgvcRniuagGCuBbleTkcPDvAWFgn3XpRSB8i+oKQhSilcNhUdHFWgeneWYjMHYuy/BwG/Ualz3qx9DMWEX1ByFJsNhVj6ZvunQW29C1mU7VTSA8i+oKQpThiRd9juHcqFyBd08LK1VcKaooWbh7C9IjoC0KWYo9172SApW+VYqgqcJPjkBr6mYqIviBkKfYYS9/qV1u7gKmSlqVfJ+maGY10NxCELMVhU4Qjxirc39pUw7KyXFaU5y3YfKxFYRLEzWzE0heELMUeU+bAm2Pn+nULW7u+LC8Hh03RUJa7oPMQpkcsfUHIUqxSDABO28Lbbx6XnZ/cexmrq9LbwEVIDhF9QchSYnXeniHFzbY2lCz0FIQZWHjzQBCEWTHO0rdnhugLmY+IviBkKZZ1b7cplBLRFxJDRF8QshSrZaIjQ1w7QnYgoi8IWYpl6YvoC8kgoi8IWYrD9OM7FqB+vpC9yNUiCFmKzXTvSBBXSAYRfUHIUhwxgVxBSBQRfUHIUs759OVjLCSOXC2CkKVYoi/uHSEZRPQFIUuxi3tHmAUi+oKQpTiilr58jIXEkatFELKUqE9f3DtCEojoC0KWcs69Ix9jIXHkahGELMXK2nGKT19IgpSKvlLqS0qpfUqpPUqpJ5VSNak8niAsJmzi3hFmQaot/a9prTdprS8Efg18PsXHE4RFg0Py9IVZkNKrRWs9GPNrLqBTeTxBWExIIFeYDSnvnKWU+jLwXmAAeGuqjycIi4VzpZXF0hcSZ85Xi1LqaaXUgThf7wTQWn9Wa10PPAh8fIp93KuU2qWU2tXV1TXXKQnCosBul9LKQvLM2dLXWt+Q4NAHgUeBL8TZx33AfQBbt24VF5AgJIBD3DvCLEh19s6qmF/fCRxJ5fEEYTFxrrSyuHeExEm1T/8flVJrgAhwBvjDFB9PEBYNDumcJcyClIq+1vqOVO5fEBYzUZ++uHeEJJDnQkHIUiRPX5gNcrUIQpYSTdkUS19IAhF9QchSrEJr4tMXkkFEXxCyFEfUpy8fYyFx5GoRhCwlmrIplr6QBCL6gpClOKSevjAL5GoRhCxFCq4Js0FEXxCyFHu0R66IvpA4IvqCkKVIu0RhNsjVIghZikMsfWEWiOgLQpZikxW5wiyQq0UQshQpuCbMBhF9QchSJHtHmA0i+oKQpZwTffkYC4kjV4sgZCni3hFmg4i+IGQpUnBNmA0i+oKQpVheHWmXKCSDXC2CkKVYlr5dLH0hCUT0BSFLcUj2jjALRPQFIUvZsqSYe69ZzpYlxQs9FSGLSGljdEEQUofHZeevblm30NMQsgyx9AVBEBYRIvqCIAiLCBF9QRCERYSIviAIwiJCRF8QBGERIaIvCIKwiBDRFwRBWESI6AuCICwilNZ6oecwDqXUEHB0oeeR4ZQB3Qs9iQxGzs/MyDmanmw8P0u11uUzDcrEFblHtdZbF3oSmYxSapeco6mR8zMzco6m53w+P+LeEQRBWESI6AuCICwiMlH071voCWQBco6mR87PzMg5mp7z9vxkXCBXEARBSB2ZaOkLgiAIKWJG0VdK1SulnlNKHVJKHVRK/Yn5eolS6iml1HHze7H5+lql1KtKqYBS6s8m7Ou0Umq/UmqPUmrXNMe8SSl1VCl1Qin1mZjXHzRfP6CUul8p5Zxi+2VKqdfM7X+qlHKZr3/a/Dv2KaWeUUotTew0Zcf5iXn/35VSw9Ns/2WlVPPEMUqpe5RSXebx9yilPpTs+ZjieBlzjpTBl5VSx5RSh5VSn5hi+7jXmlLqWqXUQMw5+vx5dn6uU0q9Yf7dDyil4mb4TfUZi3n/DqWUVkrNSwbMAp2j+5VSnUqpAxNev8ucQ2S6v2+6cUqpTeb8Dppzcc/mvMwKrfW0X0A1sMX8OR84BqwHvgp8xnz9M8BXzJ8rgEuALwN/NmFfp4GyGY5nB04Cyy9KFa4AAAa4SURBVAEXsBdYb753C6DMrx8DH51iHz8D7jZ//pY1Dngr4DV//ijw05n+/mw6P+b7W4EfAsPT7OMyc97DE16/B/jGXM9JJp8j4P3ADwCbdawp9hH3WgOuBX59Pp4fDCOwGVhtjvtb4IPJfMZi/obtwA5gazaeI3PcNcAW4MCE19cBa4Dnp/v7phqHkSq/D9hs/l4K2Of7czfV14yWvta6TWv9hvnzEHAYqAXeCTxgDnsAuN0c06m1fh0Ym2nfU7ANOKG1btRaB4GfmMdCa/2oNgF2AnUTN1ZKKeA64KE4c3tOa+0zX98Rb/tkyaTzo5SyA18D/mKGOe/QWrfN8vhJk0nnCONm/7da64h1rCnmPOO1Nl9k0PkpBYJa62PmuKeAOyZuPN1nzORLwFcA/yznN4kFOEdorbcDvXFeP6y1nnEB6TTjbgT2aa33muN6tNbh2c4zWZLy6SulGoCLgNeAyhjhaAcqE9iFBp5USu1WSt07xZhaDGvDosV8LXYeTuA9wONxti8F+rXWoam2N/kg8FgCc06YDDg/HwcemaOg36EM99dDSqn6OewnLhlwjlYAv6uU2qWUekwptWqG+ca71i5XSu01t9+QwJwTZoHPTzfgiHFF3AnEuwam/IwppbYA9Vrr3yQw11mRpnOUSlYDWin1hOlKm9ZIm28SXpGrlMoD/hf4pNZ60LjZG2ittVIqkTSgq7TWrUqpCuAppdQR826aLP8JbNdavziLbVFK/QGGG+Qts9l+in0u6PlRStUAd2G4H2bLr4Afa60DSqmPYFhO181hf+NY6HNkkgP4tdZblVK/DdwPXD3N+InX2hsYy92HlVK3AL8Apr1xJMpCnx/zGHcD/6qUygGeBBK2QJVSNuBfMNyEKWGhz9E84QCuwnA/+YBnlFK7tdbPpOPgCVn6prXzv8CDWuv/M1/uUEpVm+9XA3Efk2PRWrea3zuBh4FtZoDGCor9IdDKeOuiznzNmssXgHLg0zGvPWFu/99AD1AUE4CauP0NwGeB27TWgUT+/pnIkPNzEbASOKGUOg14lRFks8ds/7czHL8n5pz8N3BxQicgATLkHIFhlVrHfxjYZB4/9hqy5jzpWtNaD2qth82fHwWcSqmyJE5FXDLl/GitX9VaX6213obhlz9mHj+Rz1g+sBF43rwGLwMemRjEnC1pPkezmd/3zO0fnWFoC4Yh0W26mx/FiB2kBz1zMENhBL7+bcLrX2N8AOWrE97/IjEBFCAXyI/5+RXgpjjHcwCNwDLOBZk2mO99yNzOM8Ocf874INPHzJ8vwghgrZrp7070K5POz4RxUwZypxoDVMf8/C5gx/l2joB/BD5g/nwt8PoUc457rQFVnFvfsg1osn4/T85Phfk9B3gGuG6KOcf9jE0Y8zzzF8hN6zmKGd/AhEBusn/fxHFAMcYTo9f8XzwN3Dof5ymhc5nAhK/C8IHtA/aYX7dg+PWeAY6bky6J+VC0AINAv/lzAUamwF7z6yDw2WmOeQuGhXEydhwQMl+z5vH5KbZfjhF8O2FenDnm608DHTHbPzIPF2PGnJ8JY6bL3vmqedyI+f2L5uv/YB57L/AcsHZeLrIMOkdAEfAbYD/wKmYGRZzt415rGHET6xztAK44z87P1zCCpEcxXChTbR/3MzZhzPPMn+gvxDn6MdCGEQxuwcxkwjCIWoAAhp48McX2U44D/sA8/gEm3KhS/SUrcgVBEBYRsiJXEARhESGiLwiCsIgQ0RcEQVhEiOgLgiAsIkT0BUEQFhEi+oIwAaXUF9WEyowT3r9dKbU+nXMShPlCRF8Qkud2jAqPgpB1SJ6+IABKqc8C78NYxt8M7AYGgHsxVq2ewCi8diHwa/O9Ac5VofwmRskGH/BhrfWRdM5fEBJFRF9Y9CilLga+D1yKsSz+DYzSAt/TWveYY/4O6NBa/4dS6vsYNfUfMt97BvhDrfVxpdSlwD9oreetUJ0gzCcJV9kUhPOYq4GHtdlrQSn1iPn6RlPsi4A84ImJG5pVH68Afh5T8TEn5TMWhFkioi8IU/N94Hat9V6l1D3EL1ttw6gtf2Ea5yUIs0YCuYJglBC+XSnlUUrlA+8wX88H2sySvu+OGT9kvofWehA4pZS6C6I9eDenb+qCkBwi+sKiRxtt+H6KUXnxMeB1862/xujO9DIQG5j9CfDnSqk3lVIrMG4IH1RKWZUb34kgZCgSyBUEQVhEiKUvCIKwiBDRFwRBWESI6AuCICwiRPQFQRAWESL6giAIiwgRfUEQhEWEiL4gCMIiQkRfEARhEfH/ATSK/U8ntQUXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb41d2f8c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas_datareader.data as data\n",
    "from datetime import datetime\n",
    "from scipy.stats import zscore\n",
    "\n",
    "start = datetime(2015, 2, 1)\n",
    "end = datetime(2016, 1, 1)\n",
    "\n",
    "stock_time_series = data.DataReader('F', 'iex', start, end).apply(zscore)[\"open\"]\n",
    "\n",
    "stock_time_series.plot()\n",
    "len(stock_time_series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now specify the model as usual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "from brancher.standard_variables import DeterministicVariable\n",
    "\n",
    "T = len(stock_time_series)\n",
    "x0 = DeterministicVariable(stock_time_series[0], 'x0')\n",
    "x = [x0]\n",
    "names = [\"x0\"]\n",
    "for t in range(1, T):\n",
    "    names.append(\"x{}\".format(t))\n",
    "    x.append(NormalVariable(b*x[t-1], sigma, names[t]))\n",
    "AR_model = ProbabilisticModel(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can input the finance time series into our model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "for xt, value in zip(x, stock_time_series):\n",
    "    xt.observe(value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready for performing the inference. The last thing to do is to specify a variational distribution. The simplest thing to do is to \"copy\" the prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lucamb/GitRepositories/Brancher/brancher/inference.py:61: UserWarning: The inference method was not specified, using the default reverse KL variational inference\n",
      "  warnings.warn(\"The inference method was not specified, using the default reverse KL variational inference\")\n",
      "100%|██████████| 150/150 [00:39<00:00,  3.77it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Loss')"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb4451e3748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Variational distribution #\n",
    "Qnu = LogNormalVariable(0.8, 0.2, \"nu\", learnable=True)\n",
    "Qb = BetaVariable(1., 1., \"b\", learnable=True)\n",
    "variational_posterior = ProbabilisticModel([Qb, Qnu])\n",
    "AR_model.set_posterior_model(variational_posterior)\n",
    "\n",
    "# Inference #\n",
    "from brancher import inference\n",
    "\n",
    "inference.perform_inference(AR_model,\n",
    "                            number_iterations=150,\n",
    "                            number_samples=50,\n",
    "                            optimizer='Adam',\n",
    "                            lr=0.05)\n",
    "loss_list = AR_model.diagnostics[\"loss curve\"]\n",
    "plt.plot(loss_list)\n",
    "plt.title(\"Loss\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can finally plot an histogram of the posterior distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fb41cf857b8>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb41d27a748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb41cf69f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Qb.get_sample(200).hist()\n",
    "Qnu.get_sample(200).hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the autoregressive coeffient is very close to 1. This is consistent with the efficient market hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Latent time series and structured variational models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:brancherEnv]",
   "language": "python",
   "name": "conda-env-brancherEnv-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
